measuring uncertainty national bureau of … › papers › w19456.pdfbank of atlanta, the imf, nyu,...
TRANSCRIPT
NBER WORKING PAPER SERIES
MEASURING UNCERTAINTY
Kyle JuradoSydney C. Ludvigson
Serena Ng
Working Paper 19456http://www.nber.org/papers/w19456
NATIONAL BUREAU OF ECONOMIC RESEARCH1050 Massachusetts Avenue
Cambridge, MA 02138September 2013
The views expressed herein are those of the authors and do not necessarily reflect the views of theNational Bureau of Economic Research. Support from the National Science Foundation (NSF) underGrant DGE-07-07425 (Jurado) and SES-0962431 (Ng) are gratefully acknowledged. We thank NickBloom, Steve Davis, Francis Diebold, Lutz Kilian, Laura Veldkamp, seminar participants at the Bankof Canada, Columbia University, the Federal Reserve Bank of San Fransisco, the Federal ReserveBank of Atlanta, the IMF, NYU, Rutgers, UC Santa Cruz, UCLA, the 2013 High-Dimensional dataconference in Vienna, the 2013 SITE workshop, and the 2013 NBER Summer Institute for helpfulcomments. We also thank Paolo Cavallino and Daniel Greenwald for excellent research assistance.Any errors or omissions are the responsibility of the authors. The authors declare that they have norelevant or material financial interests that relate to the research described in this paper. Uncertaintyestimates and additional results are available from the website http://www.econ.nyu.edu/user/ludvigsons/jln_supp.pdf.
NBER working papers are circulated for discussion and comment purposes. They have not been peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies officialNBER publications.
© 2013 by Kyle Jurado, Sydney C. Ludvigson, and Serena Ng. All rights reserved. Short sectionsof text, not to exceed two paragraphs, may be quoted without explicit permission provided that fullcredit, including © notice, is given to the source.
Measuring UncertaintyKyle Jurado, Sydney C. Ludvigson, and Serena NgNBER Working Paper No. 19456September 2013, Revised October 2014JEL No. E0,E27,E3,E44
ABSTRACT
This paper exploits a data rich environment to provide direct econometric estimates of time-varyingmacroeconomic uncertainty, defined as the common volatility in the unforecastable component ofa large number of economic indicators. Our estimates display significant independent variations frompopular uncertainty proxies, suggesting that much of the variation in the proxies is not driven by uncertainty.Quantitatively important uncertainty episodes appear far more infrequently than indicated by popularuncertainty proxies, but when they do occur, they are larger, more persistent, and are more correlatedwith real activity. Our estimates provide a benchmark to evaluate theories for which uncertainty shocksplay a role in business cycles.
Kyle JuradoDepartment of EconomicsColumbia University440 W. 118 St.International Affairs Building, MC 3308New YorkNY [email protected]
Sydney C. LudvigsonDepartment of EconomicsNew York University19 W. 4th Street, 6th FloorNew York, NY 10002and [email protected]
Serena NgDepartment of EconomicsColumbia University440 W. 118 St.International Affairs Building, MC 3308New YorkNY [email protected]
A data appendix is available at:http://www.nber.org/data-appendix/w19456
1 Introduction
How important is time-varying economic uncertainty and what role does it play in macro-
economic fluctuations? A large and growing body of literature has concerned itself with this
question.1 At a general level, uncertainty is typically defined as the conditional volatility of a
disturbance that is unforecastable from the perspective of economic agents. In partial equilib-
rium settings, increases in uncertainty can depress hiring, investment, or consumption if agents
are subject to fixed costs or partial irreversibilities (a “real options”effect), if agents are risk
averse (a “precautionary savings”effect), or if financial constraints tighten in response to higher
uncertainty (a “financial frictions”effect). In general equilibrium settings, many of these mech-
anisms continue to imply a role for time-varying uncertainty, although some may also require
additional frictions to generate the same effects.
A challenge in empirically examining the behavior of uncertainty, and its relation to macro-
economic activity, is that no objective measure of uncertainty exists. So far, the empirical
literature has relied primarily on proxies or indicators of uncertainty, such as the implied or
realized volatility of stock market returns, the cross-sectional dispersion of firm profits, stock
returns, or productivity, the cross-sectional dispersion of subjective (survey-based) forecasts, or
the appearance of certain “uncertainty-related”key words in news publications. While most of
these measures have the advantage of being directly observable, their adequacy as proxies for
uncertainty depends on how strongly they are correlated with this latent stochastic process.
Unfortunately, the conditions under which common proxies are likely to be tightly linked
to the typical theoretical notion of uncertainty may be quite special. For example, stock mar-
ket volatility can change over time even if there is no change in uncertainty about economic
fundamentals, if leverage changes, or if movements in risk aversion or sentiment are important
drivers of asset market fluctuations. Cross-sectional dispersion in individual stock returns can
fluctuate without any change in uncertainty if there is heterogeneity in the loadings on common
risk factors. Similarly, cross-sectional dispersion in firm-level profits, sales, and productivity
can fluctuate over the business cycle merely because there is heterogeneity in the cyclicality of
firms’business activity.2
This paper provides new measures of uncertainty and relates them to macroeconomic ac-
tivity. Our goal is to provide superior econometric estimates of uncertainty that are as free as
possible both from the structure of specific theoretical models, and from dependencies on any
1See for example, Bloom (2009); Arellano, Bai, and Kehoe (2011); Bloom, Floetotto, and Jaimovich (2010);Bachmann, Elstner, and Sims (2013); Gilchrist, Sim, and Zakrajsek (2010); Schaal (2012) Bachmann and Bayer(2011); Baker, Bloom, and Davis (2011); Basu and Bundick (2011); Knotek and Khan (2011) Fernández-Villaverde, Pablo Guerrón-Quintana, and Uribe (2011); Bloom, Floetotto, Jaimovich, Saporta-Eksten, andTerry (2012); Leduc and Liu (2012); Nakamura, Sergeyev, and Steinsson (2012); Orlik and Veldkamp (2013).
2Abraham and Katz (1986) also suggested that cross-section variation in employment could vary over thebusiness cycle because of heterogeneity across firms.
1
single (or small number) of observable economic indicators. We start from the premise that
what matters for economic decision making is not whether particular economic indicators have
become more or less variable or disperse per se, but rather whether the economy has become
more or less predictable; that is, less or more uncertain.
To formalize our notion of uncertainty, let us define h-period ahead uncertainty in the
variable yjt ∈ Yt = (y1t, . . . , yNyt)′, denoted by Uyjt(h), to be the conditional volatility of the
purely unforecastable component of the future value of the series. Specifically,
Uyjt(h) ≡
√E
[(yjt+h − E[yjt+h|It])2|It
](1)
where the expectation E (·|It) is taken with respect to information It available to economicagents at time t.3 If the expectation today (conditional on all available information) of the
squared error in forecasting yjt+h rises, uncertainty in the variable increases. A measure, or
index, of macroeconomic uncertainty can then be constructed by aggregating individual uncer-
tainty at each date using aggregation weights wj :
Uyt (h) ≡ plimNy→∞
Ny∑j=1
wjUyjt(h) ≡ Ew[Uyjt(h)]. (2)
We use the terms macro and aggregate uncertainty interchangeably.
We emphasize two features of these definitions. First, we distinguish between uncertainty
in a series yjt and its conditional volatility. The proper measurement of uncertainty requires re-
moving the forecastable component E[yjt+h|It] before computing conditional volatility. Failureto do so will lead to estimates that erroneously categorize forecastable variations as “uncer-
tain.” Thus, uncertainty in a series is not the same as the conditional volatility of the raw
series where for example a constant mean is removed: it is important to remove the entire fore-
castable component. While this point may seem fairly straightforward, it is worth noting that
almost all measures of stock market volatility (realized or implied) or cross-sectional dispersion
currently used in the literature do not take this into account.4 We show below that this matters
empirically for a large number of series, including the stock market.
Second, macroeconomic uncertainty is not equal to the uncertainty in any single series yjt.
Instead, it is a measure of the common variation in uncertainty across many series. This is3A concept that is often related to uncertainty is risk. In a finance context, risk is often measured by
conditional covariance of returns with the stochastic discount factor in equilibrium models. This covariance canin turn be driven by conditional volatility in stock returns. Andersen, Bollerslev, Christoffersen, and Diebold(2012) provide a comprehensive review of the statistical measurement of the conditional variance of financialreturns. Uncertainty as defined here is (see discussion below) distinct from conditional volatility but could beone of several reasons why the conditional variances and covariances of returns vary.
4Two exceptions are Gilchrist, Sim, and Zakrajsek (2010), who use the financial factors developed by Famaand French (1992) to control for common forecastable variation in their measure of realized volatility, andBachmann, Elstner, and Sims (2013), who use subjective forecasts of analysts.
2
important because uncertainty-based theories of the business cycle typically require the exis-
tence of common (often countercyclical) variation in uncertainty across large numbers of series.
Indeed, in many models of the literature cited above, macroeconomic uncertainty is either
directly presumed by introducing stochastic volatility into aggregate shocks (e.g., shocks to
aggregate technology, representative-agent preferences, monetary or fiscal policy), or indirectly
imposed by way of a presumed countercyclical component in the volatilities of individual firm-
or household-level disturbances.5 This common variation is critical for the study of business
cycles because if the variability of the idiosyncratic shock were entirely idiosyncratic, it would
have no influence on macroeconomic variables. If these assumptions are correct, we would ex-
pect to find evidence of an aggregate uncertainty factor, or a common component in uncertainty
fluctuations that affects many series, sectors, markets, and geographical regions at the same
time.
The objective of our paper is therefore to obtain estimates of (1) and (2). To make these
measures of uncertainty operational, we require three key ingredients. First, we require an
estimate of the forecast E[yjt+h|It]. For this, we form factors from a large set of predictors
Xit, i = 1, 2, . . . , N , whose span is as close to It as possible. Using these factors, we then
approximate E[yjt+h|It] by a diffusion index forecast ideal for data-rich environments. An
important aspect of this data-rich approach is that the diffusion indices (or common factors)
can be treated as known in the subsequent analysis. Second, defining the h-step-ahead forecast
error to be V yjt+h ≡ yjt+h − E[yjt+h|It], we require an estimate of the conditional (on time t
information) volatility of this error, E[(V yt+h)
2|It]. For this, we specify a parametric stochasticvolatility model for both the one-step-ahead prediction errors in yjt and the analogous forecast
errors for the factors. These volatility estimates are used to recursively compute the values of
E[(V yt+h)
2|It] for h > 1. As we show below, this procedure takes into account an important
property of multistep-ahead forecasts, namely that time-varying volatility in the errors of the
predictor variables creates additional unforecastable variation in yjt+h (above and beyond that
created by stochastic volatility in the one-step-ahead prediction error), and contributes to its
uncertainty. The third and final ingredient is an estimate of macroeconomic uncertainty Uyt (h)
constructed from the individual uncertainty measures Uyjt(h). Our base-case estimate of Uyt (h)
is the equally-weighted average of individual uncertainties. It is also possible to let the weights
be constructed so that macroeconomic uncertainty is interpreted as the common (latent) factor
in the individual measures of uncertainty.
We estimate measures of macroeconomic uncertainty from two post-war datasets of eco-
nomic activity. The first macro dataset is monthly and uses the information in hundreds of
5See, e.g., Bloom (2009), Arellano, Bai, and Kehoe (2011), Bloom, Floetotto, and Jaimovich (2010), Gilchrist,Sim, and Zakrajsek (2010), Schaal (2012), Bachmann and Bayer (2011)). Herskovic, Kelly, Lustig, and VanNieuwerburgh (2014) find evidence of a common component in idiosyncratic volatility of firm-level cash-flowgrowth and returns.
3
macroeconomic and financial indicators. The second firm level dataset is quarterly and consists
of 155 firm-level observations on profit growth normalized by sales. We will refer to estimates
of macro uncertainty based on the monthly series as common macro uncertainty whereas es-
timates of macro uncertainty based on the quarterly firm-level dataset will be referred to as
common firm-level uncertainty.
Our main results may be summarized as follows. We find significant independent variation
in our estimates of uncertainty as compared to commonly used proxies for uncertainty. An
important finding is that our estimates imply far fewer large uncertainty episodes than what
is inferred from all of the commonly used proxies we study. For example, consider the 17
uncertainty dates defined in Bloom (2009) as events associated with stock market volatility in
excess of 1.65 standard deviations above its trend. By contrast, in a sample extending from
1960:07 to 2011:12, our measure of macro uncertainty exceeds (or come close to exceeding)
1.65 standard deviations from its mean a total of only 49 (out of 618) months, each of which
are bunched into three deep recession episodes discussed below. Moreover, our estimate of
macroeconomic uncertainty is far more persistent than stock market volatility: the response of
macro uncertainty to its own innovation from an autoregression has a half life of 53 months; the
comparable figure for stock market volatility is 4 months. Qualitatively, these results are similar
for our measures of common firm-level uncertainty in profit growth rates. Taken together, the
findings imply that most movements in common uncertainty proxies, such as stock market
volatility (the most common), and measures of cross-sectional dispersion, are not associated
with a broad-based movement in economic uncertainty as defined in (2). This is important
because it suggests that much of the variation in common uncertainty proxies is not driven by
uncertainty.
So how important is time-varying economic uncertainty, and to what extent is it dynamically
correlated with macroeconomic fluctuations? Our estimates of macro uncertainty reveal three
big episodes of uncertainty in the post-war period: the months surrounding the 1973-74 and
1981-82 recessions and the Great Recession of 2007-09. Averaged across all uncertainty forecast
horizons, the 2007-09 recession represents the most striking episode of heightened uncertainty
since 1960, with the 1981-82 recession a close second. Large positive innovations to macro uncer-
tainty lead to a sizable and protracted decline in real activity (production, hours, employment).
These effects are larger and far more persistent and do not exhibit the “overshooting”pattern
found previously when stock market volatility is used to proxy for uncertainty. Using an eleven
variable monthly macro vector autoregression (VAR) and a recursive identification procedure
with uncertainty placed last, we find that common macro uncertainty shocks account for up
to 29% of the forecast error variance in industrial production, depending on the VAR forecast
horizon. By contrast, stock market volatility explains at most 7%. To form another basis for
comparison, shocks to the federal funds rate (a common proxy for unanticipated shifts in mone-
4
tary policy) explain (at most) the same amount of forecast error variance in production as does
macroeconomic uncertainty, despite uncertainty being placed last in the VAR. Finally, we ask
how much each series’time-varying individual uncertainty is explained by time-varying macro
uncertainty and find that the role of the latter is strongly countercyclical, roughly doubling in
importance during recessions.
These results underscore the importance of considering how aggregate uncertainty is mea-
sured when assessing its relationship with the macroeconomy. In particular, our estimates imply
that quantitatively important uncertainty episodes occur far more infrequently than what is
indicated from common uncertainty proxies, but that when they do occur, they display larger
and more persistent correlations with real activity. Indeed, the deepest, most protracted re-
cessions in our sample are associated with large increases in estimated uncertainty, while more
modest reductions in real activity are not. By contrast, common uncertainty proxies are less
persistent and spike far more frequently, often in non-recession periods, or in periods of relative
macroeconomic quiescence.
While we find that increases in uncertainty are associated with large declines in real activity,
we caution that our results are silent on whether uncertainty is the cause or effect of such
declines. Our goal is to develop a defensible measure of time-varying macro uncertainty that
can be tracked over time and related to fluctuations in real activity and asset markets. Our
estimates do, however, imply that the economy is objectively less predictable in recessions than
it is in normal times. This result is not a statement about changing subjective perceptions of
uncertainty in recessions as compared to booms. Any theory for which uncertainty is entirely
the effect of recessions would need to be consistent with these basic findings.
In this way, our estimates provide a benchmark with which to evaluate theories where
uncertainty plays a role in business cycles. Uncertainty as defined in this paper only requires
evaluation of the h step ahead conditional expectation and conditional volatility of the variable
in question and so can be computed for any number of endogenous variables in a dynamic,
stochastic, general equilibrium (DSGE) model. Moreover, these statistics can be computed
from within the model regardless of whether the theory implies that uncertainty is the cause
or effect of recessions. A comparison of the uncertainty implied by the model and the data can
be used to evaluate DSGE models that feature uncertainty.
The rest of this paper is organized as follows. Section 2 reviews related empirical literature
on uncertainty in more detail. Section 3 outlines the econometric framework employed in our
study, and describes how our measures of uncertainty are constructed. Section 4 describes
the data and empirical implementation. Section 5 presents our common macro uncertainty
estimates, compares our measure to other proxies of uncertainty used in the literature, and
considers the dynamic relationship between macro uncertainty and variables such as production
and employment. Section 6 performs a similar analysis for our estimates of common firm-level
5
uncertainty. Section 7 summarizes and concludes.
To conserve space, a large amount of supplementary material for this paper appears in
Jurado, Ludvigson, and Ng (2013). This document has two parts. The first part provides results
from a large number of robustness exercises designed to check the sensitivity of our results to
various assumptions (see description below). The second part is a data appendix that contains
details on the construction of all data used in this study, including data sources. The complete
dataset used in this study, as well as the uncertainty estimates, are available for download from
the authors’website: http://www.econ.nyu.edu/user/ludvigsons/data.htm.
2 Related Empirical Literature
The literature on measuring uncertainty is still in its infancy. Existing research has primarily
relied on measures of volatility and dispersion as proxies of uncertainty. In his seminal work,
Bloom (2009) found a strong countercyclical relationship between real activity and uncertainty
as proxied by stock market volatility. His VAR estimates suggest that uncertainty has an
impact on output and employment in the six months after an innovation in these measures,
with a rise in volatility at first depressing real activity and then increasing it, leading to an
over-shoot of its long-run level, consistent with the predictions of models with uncertainty as
a driving force of macroeconomic fluctuations. Bloom, Floetotto, Jaimovich, Saporta-Eksten,
and Terry (2012) also documented a relation between real activity and uncertainty as proxied
by dispersion in firm-level earnings, industry-level earnings, total factor productivity, and the
predictions of forecasters. A recurring feature of these studies is that the uncertainty proxies
are strongly countercyclical.
While these analyses are sensible starting places and important cases to understand, we
emphasize here that the measures of dispersion and stock market volatility studied may or may
not be tightly linked to true economic uncertainty. Indeed, one of the most popular proxies for
uncertainty is closely related to financial market volatility as measured by the VIX, which has
a large component that appears driven by factors associated with time-varying risk-aversion
rather than economic uncertainty (Bekaert, Hoerova, and Duca (2012)).
A separate strand of the literature focuses on cross-sectional dispersion in NA analysts’or
firms’subjective expectations as a measure of uncertainty:
DAjt(h) =
√√√√NAt∑k=1
wAk
[(yjt+h − E(yjt+h|IAk,t))2|IAk,t
]2
where IAk,t is the information of agent k at time t, and wAk is the weight applied to agent k.
One potential advantage of using DAjt(h) as a proxy for uncertainty is that it treats the condi-
tional forecast of yjt+h as an observable variable, and therefore does not require estimation of
6
E[yt+h|IAk,t]. Bachmann, Elstner, and Sims (2013) follow this approach using a survey of Ger-man firms and argue that uncertainty appears to be more an outcome of recessions than a cause,
contrary to the predictions of theoretical models such as Bloom (2009) and Bloom, Floetotto,
Jaimovich, Saporta-Eksten, and Terry (2012). DÁmico and Orphanides (2008) is an earlier
project that studies various measures of analyst uncertainty and disagreement from the Survey
of Professional Forecasters. While analysts’forecasts are interesting in their own right, there are
several known drawbacks in using them to measure uncertainty. First, subjective expectations
are only available for a limited number of series. For example, of the 132 monthly macroeco-
nomic series we will consider in this paper, not even one-fifth have corresponding expectations
series. Second, it is not clear that the responses elicited from these surveys accurately capture
the conditional expectations of the economy as a whole. The respondents typically sampled are
practitioner forecasters; some analysts’ forecasts are known to display systematic biases and
omit relevant forecasting information (So (2012)), and analysts may have pecuniary incentives
to bias their forecasts in a way that economic agents would not. Third, disagreement in survey
forecasts could be more reflective of differences in opinion than of uncertainty (e.g., Diether,
Malloy, and Scherbina (2002); Mankiw, Reis, and Wolfers (2003)). As discussed above, it could
also reflect differences in firm’s loadings on aggregate shocks in the absence of aggregate or idio-
syncratic time-varying volatility. Fourth, Lahiri and Sheng (2010) show that, even if forecasts
are unbiased, disagreement in analysts’point forecasts does not equal (average across analysts)
forecast error uncertainty unless the variance of accumulated aggregate shocks over the forecast
horizon is zero. They show empirically using the Survey of Professional Forecasters that the
variance of the accumulated aggregate shocks can drive a large wedge between uncertainty and
disagreement in times of important economic change, or whenever the forecast horizon is not
extremely short. Bachmann, Elstner, and Sims (2013) acknowledge these problems and are
careful to address them by using additional proxies for uncertainty, such as an ex-post measure
of forecast error variance based on the survey expectations. A similar approach is taken in
Scotti (2012) who studies series for which real-time data are available. Whereas these studies
focus on variation in outcomes around subjective survey expectations of relatively few variables,
we focus on uncertainty around objective statistical forecasts for hundreds of economic series.
Our uncertainty measure is also different from proxies based on the unconditional cross-
section dispersion of a particular variable:
DBjt =
√√√√ 1
NB
NB∑k=1
[(yjkt −
1
NB
∑i
yjit)2
](3)
where yjkt is a variable indexed by j (e.g., firm-level profits studied in Bloom (2009)) for
firm k, and NB is the sample size of firms reporting profits. Notably, this dispersion has no
forward looking component; it is the same for all horizons. This measure suffers from the same
7
drawback as DAjt(h), namely that it can fluctuate without any change in uncertainty if there is
heterogeneity in the cyclicality of firms business activity.
Carriero, Clark, and Marcellino (2012) consider common sources of variation in the residual
volatilities of a Bayesian Vector Autoregression (VAR). This investigation differs from ours in
several ways: their focus is on small-order VARs (e.g., 4 or 8 variables) and residual volatility,
which corresponds to our definition of uncertainty only when h = 1; our interest is in measuring
the prevalence of uncertainty across the entire macroeconomy. Their estimation procedure
presumes that individual volatilities only have common shocks, and it is not possible for some
series to have homoskedastic shocks while others have heteroskedastic ones. We find a large
idiosyncratic component in individual volatilities, the magnitude of which varies across series.
An important unresolved issue for empirical analysis of uncertainty concerns the persistence
of uncertainty shocks. In models studied by Bloom, Floetotto, Jaimovich, Saporta-Eksten,
and Terry (2012), for example, recessions are caused by an increase in uncertainty, which in
turn causes a drop in productivity growth. But other researchers who have studied models
where uncertainty plays a key role (e.g., Schaal (2012)) have argued that empirical proxies
for uncertainty, such as the cross-sectional dispersion in firms’sales growth, are not persistent
enough to explain the prolonged levels of unemployment that have occurred during and after
some recessions, notably the 2007-2009 recession and its aftermath. Here we provide new
measures of uncertainty and its persistence, finding that they are considerably more persistent
than popular proxies such as stock market volatility and measures of dispersion.
3 Econometric Framework
We now turn to a description of our econometric framework. A crucial first step in our analysis
is to replace the conditional expectation in (1) by a forecast, from which we construct the
forecast error that forms the basis of our uncertainty measures. In order to identify a true
forecast error, it is important that our predictive model be as rich as possible, so that our
measured forecast error is purged of predictive content. A standard approach is to select a set
of K predetermined conditioning variables given by the K × 1 vector Wt, and then estimate
yt+1 = β′Wt + εt+1 (4)
by least squares. The one period forecast is yt+1|t = β′Wt where β is the least squares estimate
of β. as financial market participants have more information than that in the conditioning
variables. Indeed, recent work finds that forecasts of both real activity and financial returns
are substantially improved by augmenting best-fitting conventional forecasting equations with
common factors estimated from large datasets.6 This problem is especially important in our
6See, for example, Stock and Watson (2002b, 2004), , and Ludvigson and Ng (2007, 2009).
8
exercise since relevant information not used to form forecasts will lead to spurious estimates of
uncertainty and its dynamics.
To address this problem, we use the method of diffusion index forecasting whereby a rel-
atively small number of factors estimated from a large number of economic time series are
augmented to an otherwise standard forecasting model. The omitted information problem is
remedied by including estimated factors, and possibly non-linear functions of these factors or
factors formed from non-linear transformations of the raw data, in the forecasting model. This
eliminates the arbitrary reliance on a small number of exogenous predictors and enables the use
of information in a vast set of economic variables that are more likely to span the unobservable
information sets of economic agents. Diffusion index forecasts are increasingly used in data
rich environments. Thus we only generically highlight the forecasting step and focus instead
on construction of uncertainty, leaving details about estimation of the factors to the on-line
supplementary file.
3.1 Construction of Forecast Uncertainty
Let Xt = (X1t, . . . , XNt)′ generically denote the predictors available for analysis. It is assumed
that Xt has been suitably transformed (such as by taking logs and differencing) so as to render
the series stationary. We assume that Xit has an approximate factor structure taking the form
Xit = ΛF ′i Ft + eXit , (5)
where Ft is an rF × 1 vector of latent common factors, ΛFi is a corresponding rF × 1 vector of
latent factor loadings, and eXit is a vector of idiosyncratic errors. In an approximate dynamic
factor structure, the idiosyncratic errors eXit are permitted to have a limited amount of cross-
sectional correlation. Importantly, the number of factors rF is significantly smaller than the
number of series, N .
Let yjt generically denote a series that we wish to compute uncertainty in and whose value
in period h ≥ 1 is estimated from a factor augmented forecasting model
yjt+1 = φyj (L)yjt + γFj (L)Ft + γWj (L)Wt + vyjt+1 (6)
where φyj (L), γFj (L), and γWj (L) are finite-order polynomials in the lag operator L of orders py,
pF , and pW , respectively, the elements of the vector Ft are consistent estimates of a rotation of
Ft, and the rw dimensional vectorWt contains additional predictors that will be specified below.
An important feature of our analysis is that the one-step-ahead prediction error of yjt+1, and of
each factor Fk,t+1 and additional predictor Wh,t+1, is permitted to have time-varying volatility
σyjt+1, σFkt+1, σ
Wht+1, respectively. This feature generates time-varying uncertainty in the series
yjt.
9
When the factors have autoregressive dynamics, a more compact representation of the sys-
tem above is the factor augmented vector autoregression (FAVAR). Let Zt ≡ (F ′t ,W′t)′ be a
r = rF + rW vector which collects the rF estimated factors and rW additional predictors, and
define Zt ≡ (Z ′t, . . . , Z′t−q+1)′. Also let Yjt = (yjt, yjt−1, . . . , yjt−q+1)′. Then forecasts for any
h > 1 can be obtained from the FAVAR system, stacked in first-order companion form:
(ZtYjt
)(r+1)q×1
=
ΦZ
qr×qr0
qr×qΛ′jq×qr
ΦYj
q×q
(Zt−1
Yjt−1
)+
(VZtVYjt
)(7)
Yjt = ΦYj Yjt−1 + VYjt,
where Λ′j and ΦYj are functions of the coeffi cients in the lag polynomials in (6), ΦZ stacks
the autoregressive coeffi cients of the components of Zt.7 By the assumption of stationarity,
the largest eigenvalue of ΦYj is less than one and, under quadratic loss, the optimal h-period
forecast is the conditional mean:
EtYjt+h = (ΦYj )hYjt.
The forecast error variance at t is
ΩYjt(h) ≡ Et[(Yjt+h − EtYjt+h) (Yjt+h − EtYjt+h)′
].
Time variation in the mean squared forecast error in general arises from the fact that shocks
to both yjt and the predictors Zt may have time-varying variances. We now turn to these
implications. Note first that when h = 1,
ΩYjt(1) = Et(VYjt+1VY ′jt+1). (8)
For h > 1, the forecast error variance of Yjt+h evolves according to
ΩYjt(h) = ΦYj ΩYjt(h− 1)ΦY ′j + Et(VYjt+hVY ′jt+h). (9)
As h→∞ the forecast is the unconditional mean and the forecast error variance is the uncon-
ditional variance of Yjt. This implies that ΩYjt(h) is less variable as h increases.
We are interested in the expected forecast uncertainty of the scalar series yjt+h given in-
formation at time t, denoted Uyjt(h). This is the square-root of the appropriate entry of the
forecast error variance ΩYjt(h). With 1j being a selection vector,
Uyjt(h) =√
1′jΩYjt(h)1j. (10)
7The above specification assumes that the coeffi cients are time-invariant. Cogley and Sargent (2005) amongothers have found important variation in VAR coeffi cients. Dynamic factor models are somewhat more robust-ness against temporal parameter instability than small forecasting models (Stock and Watson (2002a)). Thereason is that such instabilities can “average out”in the construction of common factors if the instability issuffi ciently dissimilar from one series to the next. Nonetheless, as a robustness check, an uncertainty measureis also constructed using recursive out-of-sample forecasts errors and will be discussed below.
10
To estimate macro (economy-wide) uncertainty, we form weighted averages of individual
uncertainty estimates:Ny∑j=1
wjUyjt(h).
A simple weighting scheme is to give every series the equal weight of wj = 1/Ny. If individual
uncertainty has a factor structure, the weights can be defined by the eigenvector corresponding
to the largest eigenvalue of theNy×Ny covariance matrix of the matrix of individual uncertainty.
We discuss our weighting schemes for measuring macro uncertainty further below.
3.2 Time-varying Uncertainty: A Statistical Decomposition
In this subsection we show how stochastic volatility in the predictors Z and in yj contribute
to its h period ahead uncertainty. The choice of stochastic volatility is important because it
permits the construction of a shock to the second moment that is independent of innovations
to yj itself. This is consistent with much of the theoretical literature on uncertainty which
presumes the existence of a uncertainty shock that independently affects real activity. GARCH
type models (for example) do not share this feature and instead have a shock that is not
independent from innovations to yj.
Consider first the factors Ft (the argument for Wt is similar). Suppose that each Ft is
serially correlated and well represented by a univariate AR(1) model (dropping the subscript
that indexes the factor in question for simplicity):
Ft = ΦFFt−1 + vFt .
If vFt was a martingale difference with constant variance (σF )2, the forecast error variance
ΩF (h) = ΩF (h− 1) + (ΦF )2(h−1)(σF )2 increases with h but is the same for all t. We allow the
shocks to F to exhibit time-varying stochastic volatility, ie vFt = σFt εFt where log volatility has
an autoregressive structure:
log(σFt )2 = αF + βF log(σFt−1)2 + τFηFt , ηFtiid∼N(0, 1).
The stochastic volatility model allows for a shock to the second moment that is independent of
the first moment, consistent with theoretical models of uncertainty. The model implies
Et(σFt+h)
2 = exp
[αF
h−1∑s=0
(βF )s +(τF )2
2
h−1∑s=0
(βF )2(s) + (βF )h log(σFt )2
].
Since εFtiid∼(0, 1) by assumption, Et(vFt+h)
2 = Et(σFt+h)
2. This allows us to compute the h > 1
forecast error variance for F using the recursion
ΩFt (h) = (ΦF )ΩF
t (h− 1)ΦF ′ + Et(vFt+hv
F ′t+h)
11
with ΩFt (1) = Et(v
Ft+h)
2. The h period ahead predictor uncertainty at time t is the square root
of the h-step forecast error variance of the predictor:
UFt (h) =√
1′FΩFt (h)1F
where 1F is an appropriate selection vector. It follows from the determinants of E(σFt+h)2
that h-period-ahead uncertainty of Ft has a level-effect attributable to αF (the homoskedastic
variation in vFt), a scale effect attributable to τF , with persistence determined by βF .
To understand how uncertainty in the predictors affect uncertainty in the variable of interest
yj, suppose that the forecasting model for yj only has a single predictor Ft and is given by:
yjt+1 = φyjyjt + γFj Ft + vyjt+1
where vyjt+1 = σyjt+1εyjt+1 with ε
yjt+1
iid∼N(0, 1) and
log(σyjt+1)2 = αyj + βyj log(σyjt)
2 + τ yjηjt+1, ηjt+1iid∼N(0, 1).
When h = 1, V yjt+1 coincides with the innovation v
yjt+1 which is uncorrelated with the one-step-
ahead error in forecasting Ft+1, given by V Ft+1 = vFt+1. When h = 2, the forecast error for the
factor is V Ft+2 = ΦFV F
t+1 + vFt+2. The corresponding forecast error for yjt is:
V yjt+2 = vyjt+2 + φyjV
yjt+1 + γFj V
Ft+1
which evidently depends on the one-step-ahead forecasting errors made at time t, but V yt+1 and
V Ft+1 are uncorrelated. When h = 3, the forecast error is
V yjt+3 = vyjt+3 + φyjV
yjt+2 + γFj V
Ft+2
which evidently depends on V yjt+2 and V
Ft+2. But unlike the h = 2 case, the two components
V yjt+2 and V
Ft+2 are now correlated because both depend on V
Ft+1.
Therefore, returning to the general case when the predictors are Zt = (F ′t ,W′t)′ and its lags,
h-step-ahead forecast error variance for Yjt+h admits the decomposition:
ΩYjt(h) = ΦY
j ΩYjt(h− 1)ΦY ′
j
autoregressive
+ ΩZjt(h− 1)
Predictor
+ Et(VYjt+hVY ′jt+h)stochastic volatility Y
+ 2ΦYj ΩY Z
jt (h− 1)
covariance
(11)
where ΩY Zjt (h) = covt(VYjt+h,VZjt+h). The terms in E(VYj,t+hVY ′j,t+h) are computed using the fact
that Et(vyjt+h)
2 = Et(σyjt+h)
2, Et(vFt+h)2 = Et(σ
Ft+h)
2 and Et(vWt+h)2 = Et(σ
Wt+h)
2.
Time variation in uncertainty can thus be mathematically decomposed into four sources:
an autoregressive component, a common factor (predictor) component, a stochastic volatility
component, and a covariance term. Representation (11), which is equivalent to (9) for the
subvector Yt, makes clear that predictor uncertainty plays an important role via the second term
12
ΩZjt (h− 1). It is time-varying because of stochastic volatility in the innovations to the factors
and is in general non-zero for multi-step-ahead forecasts, i.e., h > 1. The role of stochastic
volatility in the series yj comes through the third term, with the role of the covariance between
the forecast errors of the series and the predictors coming through the last term. Computing
the left-hand-side therefore requires estimates of stochastic volatility in the residuals of every
series yj, and in every predictor variable Zj.
4 Empirical Implementation and Macro Data
Our empirical analysis forms forecasts and common uncertainty from two datasets. The first
dataset, denoted Xm, is an updated version of the 132 mostly macroeconomic series used in
Ludvigson and Ng (2010). The 132 macro series inXm are selected to represent broad categories
of macroeconomic time series: real output and income, employment and hours, real retail, man-
ufacturing and trade sales, consumer spending, housing starts, inventories and inventory sales
ratios, orders and unfilled orders, compensation and labor costs, capacity utilization measures,
price indexes, bond and stock market indexes, and foreign exchange measures. The second
dataset, denoted Xf , is an updated monthly version of the of 147 financial time series used
in Ludvigson and Ng (2007). The data include valuation ratios such as the dividend-price ra-
tio and earnings-price ratio, growth rates of aggregate dividends and prices, default and term
spreads, yields on corporate bonds of different ratings grades, yields on Treasuries and yield
spreads, and a broad cross-section of industry, size, book-market, and momentum portfolio
equity returns. A detailed description of the series is given in the Data Appendix of the online
supplementary file. Both of these datasets span the period 1960:01-2011:12. After lags in the
FAVAR and transformations of the raw data, we construct uncertainty estimates for the period
1960:07-2011:12, or 618 observations.
We combine the macro and financial monthly datasets together into one large “macroeco-
nomic dataset”(X) to estimate forecasting factors in these 132+147=279 series. However, we
estimate macroeconomic uncertainty Uyt (h) from the individual uncertainties in the 132 macro
series only. Uncertainties in the 147 financial series are not computed because Xm already
includes a number of financial indicators. To obtain a broad-based measure of uncertainty, it is
desirable not to over-represent the financial series, which are far more volatile than the macro
series and can easily dominate the aggregate uncertainty index.8
The stochastic volatility parameters αj, βj, τ j are estimated from the least square residuals
of the forecasting models using Markov chain Monte Carlo (MCMC) methods.9 In the base-
8The macro dataset already contains some 25 financial indicators. If we include the additional 147 indicatorsin our uncertainty index, their greater volatility will dominate the uncertainty measure and we will get back aaggregate financial market volatility variable as uncertainty.
9We use the stochvol package in R, which implements the ancillarity-suffi ciency interweaving strategy as
13
case, the average of these model parameters over the MCMC draws are used to estimate Uyjt(h).
Simple averaging is used to obtain an estimate of h period macro uncertainty denoted
Uyt (h) =1
Ny
Ny∑j=1
Uyjt(h), (12)
where the “hat”indicates the estimated value of Uyjt.This measure of average uncertainty doesnot impose any structure on the individual uncertainties above and beyond the assumed as-
sumptions on the latent volatility process.
As an alternative to equally weighting the individual uncertainty estimates, we also construct
a latent common factor estimate of macro uncertainty as the first principal component of
the covariance matrix of individual uncertainties, denoted Ut(h). To ensure that the latent
uncertainty factor is positive, the method of principal components is applied to the logarithm
of the individual uncertainty estimates and then rescaled. Its construction is detailed in the
on-line supplementary file.
Throughout, the factors in the forecasting equation are estimated by the method of static
principal components (PCA). Bai and Ng (2006) show that if√T/N → 0, the estimates Ft can
be treated as though they were observed in the subsequent forecasting regression. The defining
feature of a model with rF factors is that the rF largest population eigenvalues should increase
as N increases, while the N − rF eigenvalues should be bounded. The criterion of Bai and Ng(2002) suggests rF = 12 forecasting factors Ft for the combined datasets Xm and Xf explaining
about 54% of the variation in the 279 series, with the first three factors accounting for 37%,
8%, 3%, respectively. The first factor loads heavily on stock market portfolio returns (such as
size and book-market portfolio returns), the excess stock market return, and the log dividend-
price ratio. The second factor loads heavily on measures of real activity, such as manufacturing
production, employment, total production and employment, and capacity utilization. The third
factor loads heavily on risk and term spreads in the bond market.
The potential predictors in the forecasting model are Ft = (F1t, . . . FrF t)′ and Wt, where Wt
consists of squares of the first component of Ft, and factors inX2it collected into theNG×1 vector
Gt. These quadratic terms in Wt are used to capture possible non-linearities and any effect
that conditional volatility might have on the conditional mean function. Following Bai and Ng
(2008), the predictors ultimately used are selected so as to insure that only those likely to have
significant incremental predictive power are included. To do so, we apply a hard thresholding
rule using a conservative t test to retain those Ft andWt that are statistically significant.10 The
discussed in Kastner and Fruhwirth-Schnatter (2013) which is less sensitive to whether the mean of the volatilityprocess is in the observation or the state equation. Earlier versions of this paper implements the algorithm ofKim, Shephard, and Chib (1998) using our own MATLAB code.10Specifically, we begin with a set of candidate predictors that includes all the estimated factors in Xit (the
Ft), the first estimated factor in X2it (G1t), and the square of the first factor in Xit (F
21t). We then chose subsets
14
most frequently selected predictors are F2t, a “real”factor highly correlated with measures of
industrial production and employment, F12t−1, highly correlated with lagged hours, F4t, highly
correlated with measures of inflation, and F10t, highly correlated with exchange rates. Four lags
of the dependent variable are always included in the predictive regressions.
Before describing the results, we comment briefly on the question of whether it is desirable for
our objective to use so-called “real-time”data, which would restrict the forecasting information
set to observations on Xit that coincide with the estimated value for this series available at time
t from data collection agencies. Such a dataset differs from the final “historical”data on Xit
because initial estimates of a series are available only with a (typically one month) delay, and
earlier available estimates of many series are revised in subsequent months as better estimates
become available. In this paper we use the final revised, or historical, data in our estimation, for
two reasons. The first is a practical one: our approach calls for a summary statistic of forecasts
and therefore uncertainty across many series, requiring far more series than what is in practice
available on a real-time data basis.
Second, and more fundamentally, we are interested in forming the most historically accurate
estimates of uncertainty at any given point in time in our sample. Restricting information
to real-time data is not ideal for this objective because it is likely to be overly restrictive,
underestimating the amount of information agents actually had at the time of the forecast.
Economic modeling is replete with examples of why this could be so. In representative-agent
models, agents typically observe the current aggregate economic state as it occurs. In practice,
individuals know their own consumption, incomes, the prices they pay for consumption goods,
and probably a good deal about the output of the firm and industries they work in, long
before data collection agencies report on these. Even forecasting practitioners can predict a
large fraction of a future data release based on current information. In this sense, except
for data from asset markets, many of what is called real-time data is not really real-time
news, but instead represents newly released information on events that had occurred. Even in
heterogeneous-agent models where individuals directly observe only their own economic state
variables, the aggregate state upon which their optimization problems depend can typically
be well summarized by a few financial market returns that are observable on a timely basis.
Partly for this reason, our forecasting equations always include a large number of financial
indicators as conditioning variables. The 147 financial data series include many empirical risk-
factors for stocks and bonds that we expect to be immediately responsive to any genuine news
contained in data releases. These financial indicators can also be expected to respond in real
time to disaster-like events (wars, political shocks, natural disasters) that invariably increase
from these by running a regression of yit+1 on a constant, four lags of the dependent variable, Ft, F 21t, andG1t (no lags). Regressors are retained if they have a marginal t statistic greater than 2.575 in the multivariateforecasting regression of yit+1 on the candidate predictors known at time t.
15
uncertainty.11
5 Estimates of Macro Uncertainty
We present estimates of macro uncertainty for three horizons: h = 1, 3, and 12months. Figure 1
plots Uyt (h) over time for h = 1, 3, and 12, along with the NBER recession dates. The matching
horizontal bars correspond to 1.65 standard deviations above the mean for each series. Figure 1
shows that macro uncertainty is clearly countercyclical: the correlation of Uyt (h) with industrial
production growth is -0.62, -0.61, and -0.57 for h = 1, 3, and 12, respectively. While the level
of uncertainty increases with h (on average), the variability of uncertainty decreases because
the forecast tends to the unconditional mean as the forecast horizon tends to infinity. Macro
uncertainty exhibits spikes around the 1973-74 and 1981-82 recessions, as well as the Great
Recession of 2007-09.
Looking across all uncertainty forecast horizons h = 1, 3, and 12, the 2007-09 recession
clearly represents the most striking episode of heightened uncertainty since 1960. The 1981-82
recession is a close second, especially for forecast horizons h = 3 and 12. Indeed, for these
horizons, these are the only two episodes for which macro uncertainty exceeds 1.65 standard
deviations above its mean in our sample. Inclusive of h = 1, the three episodes are the only
instances in which Uyt (h) exceeds, or comes close to exceeding, 1.65 standard deviation above its
mean, implying far fewer uncertainty episodes than other popular proxies for uncertainty, as we
show below. Heightened uncertainty is broad-based during these three episodes as the fraction
of series with Uyjt(h) exceeding their own standard deviation over the full sample are .42, .61,
and .51 for 1, 3, and 12 respectively. Further investigation reveals that the three series with the
highest uncertainty between 1973:11 and 1975:03 are a producer price index for intermediate
materials, a commodity spot price index, and employment in mining. For the 1980:01 and
1982:11 episode, uncertainty is highest for the Fed funds rate, employment in mining, and the
3 months commercial paper rate. Between 2007:12 and 2009:06, uncertainty is highest for the
monetary base, non-borrowed reserves and total reserves. These findings are consistent with
the historical account of an energy crisis around 1974, a recession of monetary policy origin
around 1981, and a financial crisis around 2008 that created challenges for the operation of
monetary policy.
Table 1 reports summary statistics of Uyt (1).12 The table reports the first-order autocorre-
lation coeffi cient, estimates of the half-life of an aggregate uncertainty innovation from a uni-
variate autoregression (AR) for Uyt (1), estimates of skewness, and kurtosis, and IP-Corr(k)=
11Baker and Bloom (2013) use disaster-like events as instruments for stock market volatility with the objectiveof sorting out the causal relationship between uncertainty and economic growth.12The statistics for Uyjt(3) and Uyjt(12) (not reported) are very similar.
16
|corr(Uyt (1),∆IPt+k)| is the (absolute) cross-correlation of Uy
t (1) with industrial production
growth at different leads and lags, k. Also reported is the maximum of IP-Corr(k) over k. The
same statistics are reported for other uncertainty proxies, discussed below. Several statistical
facts about the estimate of aggregate uncertainty Uyt (1) stand out in Table 1.
First, the estimated half life of a shock to aggregate uncertainty is 53 months. This can
be compared to a common proxy for uncertainty, the VXO stock market volatility index con-
structed by the Chicago Board of Options Exchange (CBOE) from the prices of options con-
tracts written on the S&P 100 Index.13 The estimated half life of a shock to stock market
volatility (VXO) is 4 months. Thus, macro uncertainty is much more persistent than the most
common proxy for uncertainty, a finding relevant for theories where uncertainty is a driving force
of economic downturns, including those with more prolonged periods of below-trend economic
growth. Second, the skewness of Uyt (1) is similar to that for VXO, but the kurtosis of Uyt (1)
is lower than VXO. This implies that there are more extreme values in VXO, consistent with
the visual inspection of the two series. Third, aggregate uncertainty is strongly countercyclical
and has a contemporaneous correlation with industrial production of -0.62. Moreover, a sub-
stantial part of the comovement between aggregate uncertainty and production is attributable
to uncertainty leading real activity. The maximum of IP-Corr(k) conditional on k > 0 is -0.67
and occurs at k = 3. But there is also a substantial component of the comovement in which
uncertainty lags real activity. At negative values of k, the maximum of IP-Corr(k) is -0.59 and
occurs at k = −1. By contrast, at a one year horizon (corresponding to k = 12, 4, 2, 1 in
monthly, quarterly, semi-annual and annual data), Uyt (1) has a much stronger correlation with
future real activity than past (-0.44 versus -0.14 in monthly data), where as the opposite is true
for the cross-sectional variance of firm profits and the dispersion in subjective GDP forecasts.
Of course, these unconditional correlations are uninformative about the causal relation between
uncertainty and real activity. All that can be said is that there is a strong coherence between
uncertainty and real activity.
Uncertainty in a series is defined above as the volatility of a purely unforecastable error of
that series. It is potentially influenced by macro uncertainty shocks and idiosyncratic uncer-
tainty shocks. To assess the relative importance of macro uncertainty Uyt (h) in total uncertainty
(summed over all series), we compute, for each of the 132 series in the macro dataset
R2jτ (h) =
varτ (ϕjτ (h)Uyt (h))
varτ (Uyjt(h)). (13)
13This index is available from 1986. Following Bloom (2009), we create a longer series by splicing the CBOEVXO with estimates of realized stock market volatility for the months before 1986. Specifically, from 1961:1-1986:12, the series is the standard deviation of stock returns and from 1986:1-2011:12, the series is VXO fromthe CBOE. We refer to this spliced version as the VXO index. The VXO series is used instead of the VIXbecause the VIX data does not exist before 1990. We have also constructed a new “VIX”series that splices thepost 1990 VIX from CBOE with the standard deviation of stock returns for the earlier sample 1960: 1-1989:12and found very similar results. The correlation between VXO and VIX is 0.99 over the overlapping sample.
17
where ϕjτ (h) is the coeffi cient from a regression of Uyjt(h) on Uyt (h). Thus R2jτ (h) is the fraction
of variation in Uyjt(h) explained by macro uncertainty Uyt (h) in the subsample. The statistic is
computed for h = 1, 3, and 12, for the full sample, for recession months, and for non-recession
months.14 The larger is R2t (h) ≡ 1
Ny
∑Nyj=1R
2jt(h), the more important is macro uncertainty in
explaining total uncertainty.
Table 2 shows that the importance of macro uncertainty grows as the forecast horizon h
increases. On average across all series, the fraction of series uncertainty that is driven by
common macro uncertainty is much higher for h = 3 and h = 12 than it is for h = 1. Table
2 also shows that macro uncertainty Uyt (h) accounts for a quantitatively large fraction of the
variation in total uncertainty in the individual series. When the uncertainty horizon is h = 3
months, estimated macro uncertainty explains an average (across all series) 24%. But because
there is much more variability in uncertainty in recessions, the amount explained in recessions
is much larger (26%) than in non-recessions (16%). The results are similar for the h = 12
case. Results in the right panel of the table based on the common uncertainty factor Ut(h)
constructed by the method of principal components reinforce the point that macro uncertainty
accounts for a larger fraction of the variation in total uncertainty during recessions.
These results show that, on average across series, macro uncertainty is quantitatively im-
portant. But there is a large amount idiosyncratic variation in uncertainty across series, as
evident from the many R2t (h) statistics that are substantially lower than unity. This is also
evident from examining additional results (not in the table) on the average R2 in the lowest
and highest quartile of series. Whereas the average of R2jt(h) for h = 3 is 0.24, the upper and
lower quartiles are 0.11 and 0.37, respectively. For an uncertainty horizon of h = 12 months,
the three series that are most explained by macro uncertainty contemporaneously are: man-
ufacturing and trade inventories relative to sales, housing starts (South), and housing starts
(nonfarm), with R2 equal to 0.8, 0.8, and 0.78, respectively. The three series that are least
explained by macro uncertainty contemporaneously are: NAPM vendor deliveries index, CPI-U
(medical care), and a measure of the number of long-run unemployed (persons unemployed 27
weeks or more). All of these have R2 that are effectively zero.
5.1 The Role of the Predictors
We have emphasized the importance of removing the predictable variation in a series so as not
to attribute its fluctuations to a movement in uncertainty. How important are these predictable
variations in our estimates? Our forecasting regression is
yjt+1 = φyj (L)yjt + γFj (L)Ft + γWj (L)Wt + σyjt+1εjt+1.
14Recession months are defined by National Bureau of Economic Research dates. Macro uncertainty isestimated over the full sample even when the R2 statistics are computed over subsamples.
18
The future values of our predictors F and W are unknown and each predictor is forecasted
by an AR(4) model. As explained above, time-varying volatility in their forecast errors also
contributes to h-step-ahead uncertainty in the variable yjt whenever h > 1. Figure 2 plots
estimated factor uncertainty UFkt(h) for several estimated factors Fkt that display significant
stochastic volatility and that are frequently chosen as predictor variables according to the
hard thresholding rule. These are, F1t (highly correlated with the stock market), F2t (highly
correlated with measures of real activity such as industrial production and employment), F4t
(highly correlated with measures of inflation), F5t (highly correlated with the Fama-French risk
factors and bond default spreads). This figure also displays estimates of uncertainty for two
predictors in W : the squared value of the first factor F 21t and for the first factor formed from
observations X2it, which we denote G1t. These results suggest that uncertainty in the predictor
variables is an important contributor to uncertainty in the series yjt+h to be forecast.
In addition to the stochastic volatility effect, the predictors directly affect the level of the
forecast. An important aspect of our uncertainty measure is a forecasting model that exploits as
much available information as possible to control for the economic state, so as not to erroneously
attributing forecastable variations (as reflected in Ft and Wt) to uncertainty in series yjt+h.
Most popular measures of uncertainty do not take these systematic forecasting relationships
into account. To examine the role that this information plays in our estimates, we re-estimate
the uncertainty for each series based on the following (potentially misspecified) simple model
with constant conditional mean:
yjt+1 = µ+ σjt+1εjt+1. (14)
Figure 3 plots the resulting estimates of one-step ahead uncertainty Uyjt(1) using this possibly
misspecified model and compares it to the corresponding estimates using the full set of chosen
predictors (chosen using the hard thresholding rule described above), for several key series
in our dataset: total industrial production, employment in manufacturing, non-farm housing
starts, consumer expectations, M2, CPI-inflation, the ten-year/federal funds term spread, and
the commercial paper/federal funds rate spread. Figure 3 shows that there is substantial
heterogeneity in the time-varying uncertainty estimates across series, suggesting that a good
deal of uncertainty is series-specific. But Figure 3 also shows that the estimates of uncertainty in
these series are significantly influenced by whether or not the forecastable variation is removed
before computing uncertainty: when it is removed, the estimates of uncertainty tend to be
lower, much so in some cases. Specifically, uncertainty in each of the eight variables shown
in this figure is estimated to be lower during the 2007-09 recession when predictive content is
removed than when not, especially for industrial production, employment, and the two interest
rate spreads. The difference over time between the two estimates for these variables is quite
pronounced in some periods, suggesting that much of the variation in these series is predictable
19
and should not be attributed to uncertainty.15
Since stock market volatility is the most commonly used proxy for uncertainty, we further
examine in Figure 4 how estimates of stock market uncertainty are affected by whether or not
the purely forecastable variation in the stock market is removed before computing uncertainty.
This figure compares (i) the estimate of uncertainty in the log difference of the S&P 500
index for a case where the conditional mean is assumed constant, implying as in (14) that no
predictable variation is removed, with (ii) a case in which only autoregressive terms are included
to forecast the stock market, as in
yjt+1 = φj(L)yjt + σjt+1εjt+1,
with (iii) a case in which all selected factors (using the hard thresholding rule) estimated
from the combined macro and financial dataset with 279 indicators are used as predictors.
Notice that the first case (constant conditional mean) is most akin to estimates of stock market
volatility such as the VXO index and discussed further below. We emphasize that stock market
volatility measures do not purge movements in the stock market of its predictable component
and are therefore estimates of conditional volatility, not uncertainty. Of course, if there were
no predictable component in the stock market, these two estimates would coincide. But Figure
4 shows that there is a substantial predictable component in the log change in the S&P price
index, which, once removed, makes a quantitatively large difference in the estimated amount
of uncertainty over time.16 Uncertainty in the stock market is substantially lower in every
episode when these forecastable fluctuations are removed compared to when they are not, and
is dramatically lower in the recession of 2007-09 compared to what is indicated by ex-post
conditional stock market volatility.
If we examine more closely our measure of stock market uncertainty, (given by the baseline
estimate in Figure 4) and compare it to macro uncertainty Uyt (Figure 1), we see there areimportant differences over time in the two series. In particular, there are many (more) large
spikes in stock market uncertainty that are not present for macro uncertainty. Unlike macro
uncertainty, several of the spikes in financial uncertainty occur outside of recessions. Because
stock market volatility is arguably the most common proxy for uncertainty, we further examine
the distinction between uncertainty and stock market volatility in the next section.
15We have also re-estimated common macro uncertainty, Uyt (h) without removing predictable fluctuations.The spikes appear larger than the base case that removes the forecastable component in each series beforecomputing uncertainty. This is especially true for the h = 1 case, where presumably the predictive informationis most valuable.16Evidence for predictability of stock returns is not hard to find. Cochrane (1994) found an important
transitory component in stock prices. Ludvigson and Ng (2007) found substantial predictive information forexcess stock market returns in the factors formed from the financial dataset Xf . For more general surveys ofthe predictable variation in stock market returns, see Cochrane (2005) and Lettau and Ludvigson (2010).
20
5.2 Uncertainty Versus Stock Market Volatility
In an influential paper, Bloom (2009) emphasizes a measure of stock market volatility as a proxy
of uncertainty.17 This measure is primarily based on the VXO Index. In this subsection we
compare our macro uncertainty estimates with stock market volatility as a proxy for uncertainty.
We update this stock market volatility series to include more recent observations, and plot it
along with our estimated macro uncertainty Uyt (h) for h = 1 in Figure 5. To construct his
benchmark measure of uncertainty “shocks” (plausibly exogenous variation in his proxy of
uncertainty), Bloom selects 17 dates (listed in his Table A.1) which are associated with stock
market volatility in excess of 1.65 standard deviations above its HP-detrended mean. These 17
dates are marked by vertical lines in the figure. As emphasized above and seen again in Figure
5, Uyt (1) exceeds 1.65 standard deviations above its unconditional mean in only three episodes,
suggesting far fewer episodes of uncertainty than that indicated by these 17 uncertainty dates.18
While Uyt (1) is positively correlated with the VXO Index, with a correlation coeffi cient
around 0.5, the VXO Index is itself substantially more volatile than Uyt (1), with many sharp
peaks that are not correspondingly reflected by the macro uncertainty measure. For example,
the large spike in October 1987 reflects “Black Monday,”which occurred on the 19th of the
month when stock markets experienced their largest single-day percentage decline in recorded
history. While this may accurately reflect the sudden increase in financial market volatility
that occurred on that date, our measure of macroeconomic uncertainty barely increases at all.
Indeed, it is diffi cult to imagine that the level of macro uncertainty in the economy in October
1987 (not even a recession year) was on par with the recent financial crisis. Nevertheless, when
the VXO index is interpreted as a proxy for uncertainty, this is precisely what is implied. Other
important episodes where the two measures disagree include the recessionary period from 1980-
1982, where our measure of uncertainty was high but the VXO index was comparatively low,
and the stock market boom and bust of the late 1990s and early 2000s, where the VXO index
was high but uncertainty was low.
5.3 Macro Uncertainty and Macroeconomic Dynamics
Existing empirical research on uncertainty has often found important dynamic relationships
between real activity and various uncertainty proxies. In particular, these proxies are counter-
cyclical and VAR estimates suggest that they have a large impact on output and employment
17A number of other papers also use stock market volatility to proxy for uncertainty; these include Romer(1990), Leahy and Whited (1996), Hassler (2001), Bloom, Bond, and Van Reenen (2007), Greasley and Madsen(2006), Gilchrist, Sim, and Zakrajsek (2010), and Basu and Bundick (2011)18Bloom (2009) counts uncertainty episodes by the number of times the stock market volatility index exceeds
1.65 standard deviations above its Hodrick-Prescott filtered trend, rather than its unconditional mean. If wedo the same for Uyt (1), we find 5 episodes of heightened uncertainty: one in the early mid 1970s (1973:09 and1974:11), one during the twin recessions in the early 1980s (1980:02 and 1982:02), 1990:01, 2001:10, and 2008:07.
21
in the months after an innovation in these measures. A key result is that a in rise some proxies
(notably stock market volatility) at first depresses real activity and then increases it, leading to
an over-shoot of its long-run level, consistent with the predictions of some theoretical models
on uncertainty as a driving force of macroeconomic fluctuations.
We now use VARs to investigate the dynamic responses of key macro variables to innovations
in our uncertainty measures and compare them to the responses to innovations in the VXO
index as a proxy for uncertainty. For brevity in discussing the results, we will often refer to
these innovations to uncertainty or stock market volatility (in the case of the VXO index) as
“shocks.”As is the case of all VAR analyses, the impulse responses and variance decompositions
depend on the identification scheme, which in our case is based on the ordering of the variables.
A question arises as to which variables to include in the VAR. As a starting point, we choose a
macro VAR similar to that studied in Christiano, Eichenbaum and Evans (2005, CEE hereafter).
This VAR affords the advantage of containing a set of variables whose dynamic relationships
have been the focus of extensive macroeconomic research. Since CEE use quarterly data and we
use monthly data, we do not use exactly the same VAR, but instead include similar variables
so as to roughly cover the same sources of variation in the economy.19 We estimate impulse
responses from a eleven-variable VAR, hereafter referred to as VAR-11. The ordering mimics
that of CEE:
log (real IP)log (employment)
log (real consumption)log (PCE deflator)
log (real new orders)log (real wage)
hoursfederal funds rate
log (S&P 500 Index)growth rate of M2
uncertainty
(VAR-11)
Four versions of VARs-11 with twelve lags are considered with uncertainty taken to be either
Uyt (1) , Uyt (3), Uyt (12) , or the VXO Index. The main difference from the CEE VAR is the
inclusion of a stock price index and uncertainty. It is important to include the stock market
index for understanding the dynamics of uncertainty since it is natural to expect the two
variables to be dynamically related. In all cases, we place the measure of uncertainty last in
the VAR. The shocks to which dynamic responses are traced are identified using a Cholesky
decomposition, with the same timing assumptions made in CEE that allows identification of
19Specifically, monthly industrial production and the PCE deflator are substituted for quarterly Gross Do-mestic Product GDP and its deflator, hours is used instead of labor productivity, average hourly earnings is forthe manufacturing sector only because the aggregate measure does not go back to 1960, and the S&P 500 stockmarket index is substituted for quarterly corporate profits.
22
federal funds rate shocks.20
In addition to VAR-11, it is also of interest to compare the dynamic correlations of our
uncertainty measures with common uncertainty proxies using a VAR that has been previously
employed in the uncertainty literature. To do so, we estimate impulse responses from a eight-
variable model as in Bloom (2009), hereafter referred to as VAR-8:
log(S&P 500 Index)uncertainty
federal funds ratelog(wages)log(CPI)
hourslog(employment)
log(industrial production)
. (VAR-8)
Following Bloom (2009), VAR-8 uses twelve lags of industrial production, wages, hours. Unlike
VAR-11, VAR-8 uses employment for the manufacturing sector only. Bloom (2009) considers a
15-point shock to the error in the VXO equation. This amounts to approximately 4 standard
deviations of the identified error. We record responses to 4 standard deviation shocks in Uyt (h),
so the magnitudes are comparable with those of VXO shocks. However, we make one departure
from the estimates in Bloom (2009). We do not detrend any variables using the filter of Hodrick
and Prescott (1997), while Bloom did so for every series except the VXO index. Because the
HP filter uses information over the entire sample, it is diffi cult to interpret the timing of an
observation.21
Figure 6 shows the dynamic responses of output and employment in VAR-11. Shocks to
Uyt (h) sharply reduce production and employment, with the effects persisting well past the
60 month horizon depicted. The last row of this figure compares the responses when the
VXO index is used as a proxy for uncertainty. Both the magnitude and the persistence of the
responses of production and employment are much smaller. The responses to Uyt (h) are far more
protracted than those to the VXO Index, which underscores the greater persistence of these
measures as compared to popular uncertainty proxies. Indeed, the response of employment
to a VXO disturbance is barely statistically different from zero shortly after the shock and
outright insignificant at other horizons. The response of production to a VXO shock is also only
marginally different from zero for the first 3 months, becoming zero thereafter. An important
difference in these results from those reported in Bloom (2009) is that shocks to any of these
measures (including VXO) do not generate a statistically significant “volatility overshoot,”
20We have confirmed that the dynamic responses of the non-uncertainty variables to a federal funds rate shock(interpreted by CEE as a monetary policy shock) in a VAR that does not include any uncertainty measure arequalitatively and quantitatively very similar to those reported in CEE. These results are available upon request.21Results using HP filtered data and the original Bloom VAR are reported in the on-line supplementary
material file for this paper.
23
namely, the rebound in real activity following the initial decline after a positive uncertainty
shock. This finding echoes those in Bachmann, Elstner, and Sims (2013). Unlike the findings
in Bachmann, Elstner, and Sims (2013), however, the short-run (within 10 months) responses
to our uncertainty shocks are sizable.
Figure 7 shows the dynamic responses of output and employment in VAR-8. The responses of
these variables, both in terms of magnitude and persistence, to the macro uncertainty measures
Uyt (h) are similar to those reported in Figure 6 using VAR-11. Disturbances to the VXO index
appear to have larger and somewhat more persistent effects in VAR-8 than in VAR-11. But the
responses to VXO shocks even in this VAR are not as large or persistent as those to innovations
in macro uncertainty Uyt (h). Again, there is no clear evidence of a volatility overshoot in
response to any of the uncertainty measures, including VXO. The overshoot found by Bloom
(2009) appears to be sensitive to whether the VXO data are HP filtered.22
To study the quantitative importance of uncertainty shocks for macroeconomic fluctuations,
Table 3 reports forecast error variance decomposition for production, employment and hours and
compares them with the decompositions when VXO is used instead as the proxy for uncertainty
in the VAR-11. We use k here to distinguish the VAR forecast horizon from the uncertainty
forecast horizon h. The table shows the fraction of the VAR forecast error variance that is
attributable to common macro uncertainty shocks in Uyt (h) over several horizons, including the
horizon k for which shocks to the uncertainty measure Uyt (1) or VXO are associated with the
greatest fraction of VAR forecast error variance (denoted k =max in the table). The table also
reports the fraction of variation attributable to the federal funds rate, which we discuss below.
From Table 3 we can see that uncertainty shocks are associated with much larger fractions
of real activity than are VXO shocks. Shocks to Uyt (12), for example, are associated with a
maximum of 29% of the forecast error variance in production, 31% of the forecast error variance
in employment, and 12% of the forecast error variance in hours. By contrast, the corresponding
numbers for VXO shocks are 6.9%, 7.6%, and 2.3%, respectively. Thus, uncertainty shocks are
associated with over four times the variation in production and employment and over five times
the variation in hours compared to VXO shocks.
To put these results in perspective, Table 3 also reports the fraction of variation in these
variables that is attributable to monetary policy shocks, identified here following CEE by a
shock in VAR-11 to the federal funds rate. Inn the VAR-11 where Uyt (12) is included as the
measure of uncertainty, shocks to the federal funds rate are associated with a maximum of 29%
of the forecast error variance in production, 32% of the forecast error variance in employment,
and 10% of the forecast error variance in hours. These numbers are almost identical to the
fraction explained by shocks to Uyt (12). This finding suggest that the dynamic correlation of
22After a careful inspection of the code kindly provided by Bloom, we find that contrary to a statement inthe paper, Bloom (2009) HP filters all data in the VAR for these impulse responses except the VXO index.
24
uncertainty with the real economy may be quantitatively as important as it is for monetary
policy shocks.
We can use the same variance decompositions to ask how much of uncertainty variation is
associated with variation in innovations of the other variables in the system. These results are
not reported in the table, but we discuss a few of them here. At the k =∞ horizon, we find that
stock return innovations are associated with the largest fraction of variation in Uyt (12), equal
to 15.26%, followed by price level innovations (11.9%) and innovations to industrial production
(9.56%). These numbers are roughly of the same order of magnitude as those for the fraction of
forecast error variance in production growth explained by Uyt (12) for k =∞ (equal to 15.75%).
These variance decompositions are of course specific to the ordering of the variables used in
the analysis. But as uncertainty is placed last in the VAR, the effects of uncertainty shocks
on the other variables in the system are measured after we have removed all the variation in
uncertainty that is attributable to shocks to the other endogenous variables in the system. That
the effects of uncertainty shocks are still non-trivial is consistent with the view that uncertainty
has important implications for economic activity.
These variance decomposition results are similar if we instead use VARs that include both
VXO and our uncertainty measures Uyt (h). From such VARs, we find that the big driver of
VXO are shocks to VXO, not uncertainty. This reinforces the conclusion that stock market
volatility is driven largely by shocks other than those to broad-based economic uncertainty,
suggesting researchers should be cautious when using this measure as a proxy for uncertainty.
We have reported results only for the base-case estimates described above. An on-line sup-
plementary file provides additional results designed to check the sensitivity of our results to
various assumptions made above. These exercises are based on (i) alternative weights used to
aggregate individual uncertainty series; (ii) alternative location statistics of stochastic volatility
to construct individual uncertainty series; (iii) alternative conditioning information based on
recursive (out-of-sample) forecasts to construct diffusion index forecasts (iv) alterative measures
of volatility of individual series such as GARCH and EGARCH.23 The key findings are qualita-
tively and quantitatively similar to the ones reported here. We note one finding in particular,
namely that the results above are not sensitive to whether we use out-of-sample (recursive) or
in-sample forecasts; indeed the correlation between the resulting uncertainty measures is 0.98.24
23Results based on the GARCH/EGARCH estimates indicate the number and timing of big uncertaintyepisodes, as well as the persistence of uncertainty, is very similar to what is found using our base-case measure ofmacro uncertainty. What is different is the real effect of uncertainty innovations from a VAR, once orthogonalizedshocks are analyzed. This is to be expected because GARCH type models (unlike stochastic volatility) havea shock to the second moment that is not independent of the first moment, a structure inconsistent with theassumptions of an independent uncertainty shock presumed in the uncertainty literature. Using a GARCH-baseduncertainty index thus creates additional identification problems that are beyond the scope of this paper.24Note also that, in the recursive forecast estimation the parameters of the forecasting relation change every
period, so this speaks directly to the question of the role played by parameter stability in our estimates,suggesting that parameter instability is not important in our FAVAR.
25
5.4 Comparison with Measures of Dispersion
This subsection compares the time-series behavior of Uyt (h) with four cross-sectional uncertainty
proxies studied by Bloom (2009). These are:
1. The cross-sectional dispersion of firm stock returns. This is defined as the within-month
cross-sectional standard deviation of stock returns for firms with at least 500 months of
data in the Center for Research in Securities Prices (CRSP) stock-returns file. The series
is also linearly detrended over our sample period.
2. The cross-sectional dispersion of firm profit growth. Profit growth rates are normalized
by average sales on a monthly basis, so that this measure captures the quarterly cross-
sectional standard deviation profits. We formulate a year-over-year version to minimize
seasonal variation equal to profitsit−profitsit−40.5(salesit+salesit−4)
, where i = 1, 2, . . . , Nt indexes the firms and
Nt denotes the total number of firms observed in month t. The sample is restricted to
firms with at least 150 quarters of data in the Compustat (North America) database.
3. The cross-sectional dispersion of GDP forecasts from the Philadelphia Federal Reserve
Bank’s biannual Livingston Survey. This is defined as the biannual cross-sectional stan-
dard deviation of forecasts of nominal GDP one year ahead. The series is also linearly
detrended over our sample period.
4. The cross-sectional dispersion of industry-level total factor productivity (TFP). This is
defined as the annual cross-sectional standard deviation of TFP growth rates within SIC
4-digit manufacturing industries, calculated using the five-factor TFP growth data com-
puted by Bartelsman, Becker, and Gray as a part of the NBER-CES Manufacturing
Industry Database (http://www.nber.org/data/nbprod2005.html).25
These updated series, along with Uyt (1) are displayed in Figure 8. As was true in the case
of stock market volatility in the previous subsection, these measures exhibit quite different
behavior from macroeconomic uncertainty. Stock return dispersion tells a story roughly similar
to the VXO Index, with a particularly large increase in uncertainty leading up to the 2001
recession that is not present in our measure of macro uncertainty. Firm profit dispersion
actually suggests a relatively low level of uncertainty during the 1980-82 recessions when macro
uncertainty was high, with a sharp increase towards the end of the 1982 recession, by which time
macro uncertainty had declined. GDP forecast dispersion points to a level of uncertainty during
each of the 1969-70 and 1990 recessions which is on par with the level of uncertainty during
25There is a jump in the 1997 industry TFP dispersion measure that occurs purely because of a move fromNAICS to SIC industry classification codes. We therefore drop this year and interpolate to obtain the continuouspanel.
26
the 2007-09 recession. Again, this contrasts with macro uncertainty which is at a record high
in the 2007-09 recession but was not high in the previous episodes. Industry TFP dispersion
shows almost no increase in uncertainty during the 1980-82 recessions. and displays the largest
increase during the recent financial crisis.
It is instructive to consider the different statistical properties of these dispersion measures
as they compare to those for the estimated aggregate uncertainty index. Table 1 provides the
statistics. To match the frequency of the dispersion measure, we aggregate our monthly series
Uyt (h) using averages over the desired period.
The statistics using these proxies for uncertainty paint a similar picture to that obtained
using the VXO Index. In particular, the responses of Uyt (1) to its own shock from an autore-
gression are far more prolonged than those of the dispersion proxies. For example, the response
of the dispersion in firm-level stock returns to its own shock has a half-life of 1.9 months,
compared to 52.5 months for Uyjt(1).
We also consider impulse responses of production and employment for the eleven-variable
VAR, but using these measures of dispersion as the proxy for uncertainty. These results are
reported in Figure 9 and can be summarized as follows. The dynamic responses using dispersions
to proxy for uncertainty do not in general display the intuitive pattern that production and
employment should fall as a result of an uncertainty shock. Production falls the most on impact
in response to shocks to the cross-sectional dispersion in industry-level TFP, but the response
of employment is more muted. In the case of stock return dispersion, we see no statistically
significant response in production or employment to an innovation. Shocks to the dispersion
in firm profits lead to an increase in production and employment, as do shocks to the cross-
sectional dispersion in subjective GDP forecasts.
Overall, these results show that, like the VXO proxy, increases in measures of cross-sectional
dispersion do not necessarily coincide with increases in broad-based macro uncertainty, where
the latter is associated with a large and persistent decline in real activity. Like stock market
volatility over time, measures of dispersion may vary for many reasons that are unrelated to
broad-based macroeconomic uncertainty.
6 Results: Firm-Level Common Uncertainty
In this section we turn from our analysis of common macroeconomic uncertainty to examine
common variation in uncertainty at the firm level. Rather than studying uncertainty across
many different variables, we now study uncertainty on the same variable across many different
firms. Specifically, we measure uncertainty in the profit growth of individual firms. For the
firm-level dataset, the unit of observation is the change in firm pre-tax profits Pi,t, normalized
by a two-period moving average of sales, Si,t, following Bloom (2009). Given the seasonality
27
in this series, we instead form a year-over-year version of this measure, as detailed in the data
appendix. After converting to a balanced panel, we are left with 155 firms from 1970:Q1-
2011:Q2 without missing values.26 With data transformations and lags in the FAVAR, we are
left with uncertainty estimates for 1970:Q3-2011:Q2. For each firm, the series to be forecast is
normalized pretax profits, so again yit = Xit. For the firm-level results, as for the macro results,
we form forecasting factors Ft from the panel XitNxpi=1 , as well as X2it
Nxpi=1 where Nxp = 155, the
number of cross-sectional firm-level observations. We find evidence of two factors in XitNxpi=1
and one factor in X2it
Nxpi=1 . The Wt vector of additional predictors includes the macro factors
estimated from the macro data set. As before, a conservative t test is used to include only the
predictors that are statistically significant.
One important consideration that is relevant to this microeconomic context is the construc-
tion of our panel. Since we need a reasonable number of time series observations to estimate
the stochastic volatility processes, we require that the panel be balanced. This leads us to drop
about 400 firms per quarter on average. In particular, many of the firms operating towards
the beginning of our sample are excluded, because they do not survive until 2011:Q2. This
eliminates a large fraction of the cross-sectional variation before 1995. Because of this survivor-
ship bias, it is diffi cult to conclude that our estimated aggregate firm-level uncertainty measure
represents a comprehensive measure of the uncertainty facing firms since 1970. But note that
we will compute the cross-sectional standard deviation of firm profits within this same balanced
panel and compare it to our estimate of common firm-level uncertainty from the panel. Since
the two measures are computed over the same panel of firms, any differences between them
cannot be attributable to survivorship bias.
Figure 10 displays the estimated common uncertainty in firm-level profits Uyt (h) over time
for h = 1, 3, and 4 quarters. Like the measure of macroeconomic uncertainty analyzed above,
these estimates point to a rise in uncertainty surrounding the 1973-75,1980-82 recessions, but
not of the same magnitude. Instead, there are larger increases in common firm-level uncertainty
surrounding the 2000-01 and 2007-09 recessions. However, this type of aggregate uncertainty
is less countercyclical: the correlation of each of these measures with industrial production
growth is negative, but smaller in absolute value than is the correlation of the macro uncertainty
measures with production growth. This figure also compares our measures of common firm-level
uncertainty Uyt (h) to the popular proxy for common firm-level uncertainty given by on the cross-
sectional dispersion in firm profit growth normalized by sales, denoted DBt (see equation (3)).As the figure shows, the two measures behave quite differently, with many more spikes in DBtthan in common firm-level uncertainty. Indeed, the dispersion measure exceeds 1.65 standard
26A limitation with Compustat data is that its coverage is restricted to large publicly traded firms. TheCensus Bureau’s ASM data are more comprehensive, but limited to annual observations. Similarly, (industrylevel) total factor productivity may be preferred over profits as the source of uncertainty, but these industrylevel data eliminate much of the uncertainty at the firm level (Schaal (2012)).
28
deviations above its mean dozens of times, while common firm-level uncertainty measures only
do so a handful of times. Like the VXO index, there appear to be many movements in the
cross-sectional standard deviation of firm profit growth that are not driven by common shocks
to uncertainty across firms.
To assess the relative importance of macro uncertainty Uyt (h) in total uncertainty, we again
compute, for each of the 155 firms in the firm-level dataset, and for h = 1 to 6, the R2jt(h)
as defined in (13), averaged over t. As above, this exercise is performed for the full sample,
for recession months, and for non-recession months. Table 4 shows that common firm-level
uncertainty comprises a larger fraction of the variation in total uncertainty during recessions
that during non-recessions, as was the case for common macroeconomic uncertainty. Indeed,
the common firm-level common uncertainty we estimate explains an average of 18% of the
variation in total uncertainty for an uncertainty horizon of h = 4 quarters in non-recessions,
but it explains double that in recessions. These results echo those using the macro uncertainty
measures. Other results (using VARs for example) are qualitatively similar and omitted to
conserve space.
7 Conclusion
In this paper we have introduced new time series measures of macroeconomic uncertainty. We
have strived to ensure that these measures be comprehensive and as free as possible from both
the restrictions of theoretical models and/or dependencies on a handful of economic indicators.
We are interested in macroeconomic uncertainty, namely uncertainty that may be observed
in many economic indicators at the same time, across firms, sectors, markets, and geographic
regions. And we are interested in the extent to which this macroeconomic uncertainty is asso-
ciated with fluctuations in aggregate real activity and financial markets.
Our measures of macroeconomic uncertainty fluctuate in a manner that is often quite distinct
from popular proxies for uncertainty, including the volatility of stock market returns (both over
time and in the cross-section), the cross-sectional dispersion of firm profits, productivity, or
survey-based forecasts. Indeed, our estimates imply far fewer important uncertainty episodes
than do popular proxies such as stock market volatility, a measure that forms the basis for the
17 uncertainty dates identified by Bloom (2009). By contrast, we uncover just three big macro
uncertainty episodes in the post-war period: the months surrounding the 1973-74 and 1981-82
recessions and the Great Recession of 2007-09, with the 2007-09 recession the most striking
episode of heightened uncertainty since 1960. These findings and others reported here suggest
that there is much variability in the stock market and in other uncertainty proxies that is not
generated by a movement in genuine uncertainty across the broader economy. This occurs both
because these proxies over-weight certain series in the measurement of macro uncertainty, and
29
because they erroneously attribute forecastable fluctuations to a movement in uncertainty.
Our estimates nevertheless point to a quantitatively important dynamic relationship be-
tween uncertainty and real activity. In an eleven variable monthly macro VAR, common macro
uncertainty shocks have effects on par with monetary policy shocks and are associated with a
much larger fraction of the VAR forecast error variance in production and hours worked than are
stock market volatility shocks. Our estimates also suggest that macro uncertainty is strongly
countercyclical, explaining a much larger component of total uncertainty during recessions than
in non-recessions, and far more persistent than common uncertainty proxies.
In this paper we have deliberately taken an atheoretical approach, in order to provide a
model-free index of macroeconomic uncertainty that can be tracked over time. Such an in-
dex can be used as a benchmark for evaluating any DSGE model with (potentially numerous)
primitive stochastic volatility shocks. Our measure of uncertainty conveniently aggregates un-
certainty in the economy derived from all sources into one summary statistic. In some cases, it
may be useful to construct sub-indices. These can be easily constructed using our framework.
ReferencesAbraham, K. G., and L. F. Katz (1986): “Cyclical Unemployment: Sectora Shifts orAggregate Demand?,”The Journal of Political Economy, 94(3), 507—522.
Andersen, T. G., T. Bollerslev, P. F. Christoffersen, and F. X. Diebold (2012):“Financial Risk Measurement for Financial Risk Management,” in Handbook of the Eco-nomics of Finance Vol. II, forthcoming, ed. by G. Constantinides, M. Harris, and R. Stulz.Elsevier Science B.V., North Holland, Amsterdam.
Arellano, C., Y. Bai, and P. Kehoe (2011): “Financial Markets and Fluctuations inUncertainty,”Federal Reserve Bank of Minneapolis Research Department Staff Report.
Bachmann, R., and C. Bayer (2011): “Uncertainty Business Cycles — Really?,” WPNBER17315.
Bachmann, R., S. Elstner, and E. R. Sims (2013): “Uncertainty and Economic Activity:Evidence from Business Survey Data,” American Economic Journal: Macroeconomics, 5,217—249.
Bai, J., and S. Ng (2002): “Determining the Number of Factors in Approximate FactorModels,”Econometrica, 70(1), 191—221.
(2006): “Confidence Intervals for Diffusion Index Forecasts and Inference for Factor-Augmented Regressions,”Econometrica, 74(4), 1133—1150.
(2008): “Forecasting Economic Time Series Using Targeted Predictors,” Journal ofEconometrics, 146, 304—317.
Baker, S. R., and N. Bloom (2013): “Does Uncertainty Reduce Growth? Using Disastersas Natural Experiments,”NBER Working Paper No. 19475.
Baker, S. R., N. Bloom, and S. J. Davis (2011): “Measuring Economic Policy Uncertainty,”Unpublished paper, Stanford University.
Basu, S., and B. Bundick (2011): “Uncertainty Shocks in a Model of Effective Demand,”Unpublished paper, Boston College.
Bekaert, G., M. Hoerova, and M. L. Duca (2012): “Risk, Uncertaintyand Monetary Policy,” Available at SSRN: http://ssrn.com/abstract=1561171 orhttp://dx.doi.org/10.2139/ssrn.1561171.
Bloom, N. (2009): “The Impact of Uncertainty Shocks,”Econometrica, 77, 623—685.
Bloom, N., S. Bond, and J. Van Reenen (2007): “Uncertainty and Investment Dynamics,”Review of Economic Studies, 74(2), 391—415.
Bloom, N., M. Floetotto, and N. Jaimovich (2010): “Really Uncertain Business Cycles,”Mimeo, Standford University.
Bloom, N., M. Floetotto, N. Jaimovich, I. Saporta-Eksten, and S. J. Terry (2012):“Really Uncertain Business Cycles,”WP NBER18245.
Carriero, A., T. E. Clark, and M. Marcellino (2012): “Common Drifting Volatility inLarge Bayesian VARs,”Working Paper12-06, Federal Reserve Bank of Cleveland.
Christiano, L. J., M. Eichenbaum, and C. L. Evans (2005): “Nominal Rigidities andthe Dynamic Effects of a Shock to Monetary Policy,”Journal of Political Economy, 113(1),1—45.
Cochrane, J. H. (1994): “Permanent and Transitory Components of GDP and Stock Prices,”Quarterly Journal of Economics, 109, 241—265.
(2005): Asset Pricing, Revised Edition. Princeton University Press, Princeton, NJ.
Cogley, T., and T. J. Sargent (2005): “Drifts and Volatilities: Monetary Policies andOutcomes in the Post WWII US,”Review of Economic Dynamics, 8(2), 262—302.
DÁmico, S., and A. Orphanides (2008): “Uncertainty and Disagreement in Economic Fore-casting,”Finance and Economics Discussion Series, Federal Reserve Board.
Diether, K. B., C. J. Malloy, and A. Scherbina (2002): “Differences of Opinion andthe Cross Section of Stock Returns,”The Journal of Finance, 57(5), 2113—2141.
Fama, E. F., and K. R. French (1992): “The Cross-Section of Expected Returns,”Journalof Finance, 47, 427—465.
Fernández-Villaverde, J., J. F. R.-R. Pablo Guerrón-Quintana, and M. Uribe(2011): “Risk Matters: The Real Effects of Volatility Shocks,”American Economic Review,6(101), 2530—2561.
Gilchrist, S., J. W. Sim, and E. Zakrajsek (2010): “Uncertainty, Financial Frictions, andInvestment Dynamics,”Unpublished Manuscript, Boston University.
Greasley, D., and J. B. Madsen (2006): “Investment and Uncertainty: Precipitating theGreat Depression in the United States,”Economica, 73(291), 393—412.
Hassler, J. (2001): “Uncertainty and the Timing of Automobile Purchases,” ScandinavianJournal of Economics, 103(2), 351—366.
Herskovic, B., B. Kelly, H. Lustig, and S. Van Nieuwerburgh (2014): “The CommonFactor in Idiosyncratic Volatility: Quantitative Asset Pricing Implications,” UnpublishedPaper, New York University.
Hodrick, R., and E. C. Prescott (1997): “Post-War U.S. Business Cycles: A DescriptiveEmpirical Investigation,”Journal of Money, Credit, and Banking, 29, 1—16.
Jurado, K., S. C. Ludvigson, and S. Ng (2013): “Measuring Uncertainty: SupplementaryMaterial,”Unpublished paper, Columbia University.
Kastner, G., and S. Fruhwirth-Schnatter (2013): “Ancillarity-suffi ciency interweavingstrategy (ASIS) for boosting MCMC estimation of stochastic volatility models,”Computa-tional Statistics and Data Analysis, forthcoming.
Kim, S., N. Shephard, and S. Chib (1998): “Stochastic Volatility: Likelihood Inference andComparison with ARCH Models,”The Review of Economic Studies, 65(3), 361—393.
Knotek, E. S., and S. Khan (2011): “How Do Households Respond to Uncertainty Shocks?,”Federal Reserve Bank of Kansas City Economic Review.
Lahiri, K., and X. Sheng (2010): “Measuring Forecast Uncertainty By Disagreement: TheMissing Link,”Journal of Applied Econometrics, 25, 514—538.
Leahy, J. V., and T. M. Whited (1996): “The Effect of Uncertainty on Investment: SomeStylized Facts,”Journal of Money, Credit and Banking, 28(1), 64—83.
Leduc, S., and Z. Liu (2012): “Uncertainty Shocks are Aggregate Demand Shocks,”FederalReserve Bank of San Francisco, Working Paper 2012-10.
Lettau, M., and S. C. Ludvigson (2010): “Measuring and Modeling Variation in the Risk-Return Tradeoff,”in Handbook of Financial Econometrics, ed. by Y. Ait-Sahalia, and L. P.Hansen, vol. 1, pp. 617—690. Elsevier Science B.V., North Holland, Amsterdam.
Ludvigson, S. C., and S. Ng (2007): “The Empirical Risk-Return Relation: A FactorAnalysis Approach,”Journal of Financial Economics, 83, 171—222.
(2009): “Macro Factors in Bond Risk Premia,” The Review of Financial Studies,22(12), 5027—5067.
(2010): “A Factor Analysis of Bond Risk Premia,”inHandbook of Empirical Economicsand Finance, ed. by A. Ulah, and D. E. A. Giles, vol. 1, pp. 313—372. Chapman and Hall,Boca Raton, FL.
Mankiw, G. N., R. Reis, and J. Wolfers (2003): “Disagreement About Inflation Expec-tations,” in National Bureau of Economic Research Macroeconomics Annual, 2003, ed. byM. Gertler, and K. Rogoff, pp. 209—248. MIT Press, Cambridge, MA.
Nakamura, E., D. Sergeyev, and J. Steinsson (2012): “Growth-Rate and UncertaintyShocks in Consumption: Cross-Country Evidence,”Working Paper, Columbia University.
Orlik, A., and L. Veldkamp (2013): “Understanding Uncertainty Shocks,” Unpublishedmanuscript, New York University Stern School of Business.
Romer, C. D. (1990): “The Great Crash and the Onset of the Great Depression,”QuarterlyJournal of Economics, 105(3), 597—624.
Schaal, E. (2012): “Uncertainty, Productivity, and Unemployment in the Great Recession,”Unpublished paper, Princeton University.
Scotti, C. (2012): “Surprise and Uncertainty Indexes: Real-time Aggregation of Real-ActivityMacro Surprises,”Unpublished paper, Federal Reserve Board.
So, E. (2012): “A New Approach to Predicting Analyst Forecast Errors: Do Investors Over-weight Analyst Forecasts?,”Journal of Financial Economics, forthcoming.
Stock, J. H., and M. W. Watson (2002a): “Forecasting Using Principal Components Froma Large Number of Predictors,” Journal of the American Statistical Association, 97(460),1167—1179.
(2002b): “Macroeconomic Forecasting Using Diffusion Indexes,”Journal of Businessand Economic Statistics, 20(2), 147—162.
(2004): “Forecasting with Many Predictors,”Unpublished paper, Princeton University.
Uncertainty measured byStatistic (Monthly) VXO D(Returns) Uyt (1)AR(1), Half life 0.85, 4.13 0.70, 1.92 0.99, 53.58Skewness, Kurtosis 2.18, 11.05 1.30, 5.51 1.81, 7.06IP-Corr(0) -0.32 -0.45 -0.62IP-Corr(12), IP-Corr(-12) -0.29,-0.11 -0.25,-0.07 -0.44,-0.14maxk>0IP-Corr(k) -0.43 -0.47 -0.67At lag k = 6 2 3
maxk<0IP-Corr(k) -0.30 -0.43 -0.59At lag k = -1 -1 -1
Statistic (Quarterly) D(Profits) Uyt (1)AR(1), Half life 0.76, 2.55 0.93, 10.23Skewness, Kurtosis 0.36, 2.47 1.77, 6.75IP-Corr(0) -0.37 -0.64IP-Corr(4), IP-Corr(-4) -0.11,-0.30 -0.46,-0.16maxk>0IP-Corr(k) -0.34 -0.70At lag k = 1 1
maxk<0IP-Corr(k) -0.37 -0.53At lag k = -1 -1
Statistic (Semi-Annual) D(Forecasts) Uyt (1)AR(1), Half Life 0.45, 0.86 0.85, 4.18Skewness, Kurtosis 0.24, 2.19 1.74, 6.41IP-Corr(0) -0.41 -0.64IP-Corr(2), IP-Corr(-2) -0.16,-0.24 -0.48,-0.16maxk>0IP-Corr(k) -0.34 -0.68At lag k = 1 1
maxk<0IP-Corr(k) -0.35 -0.40At lag k = -1 -1
Statistic (Annual) D(TFP) Uyt (1)AR(1), Half Life 0.33, 0.63 0.61, 1.40Skewness, Kurtosis 1.71, 8.56 1.76, 6.24IP-Corr(0) -0.55 -0.69IP-Corr(1), IP-Corr(-1) -0.33,-0.09 -0.48,-0.16maxk>0IP-Corr(k) -0.33 -0.47At lag k = 1 1
maxk<0IP-Corr(k) -0.24 -0.24At lag k = -26 -26
Table 1: Summary Statistics. This table displays a number of summary statistics characterizing variousproxies. IP-Corr(k) is the absolute cross-correlation coeffi cient between a measure of uncertainty ut and 12month moving average of industrial production growth in period t+ k, ie. IP-Corr(k)=|corr(ut,∆lnIPt+k)|. Apositive k means uncertainty is correlated with future IP. Half-lifes are based on estimates from a univariateAR(1) model for each series. The maximum correlation, at different leads/lags, with the growth rate of IP(12 month moving average) is also reported. Uyt (1) denotes base case estimated aggregate uncertainty. D(·)represents dispersion, i.e. the cross-sectional standard deviation. Monthly series are aggregated to quarterly,semi-annual, and annual series by averaging monthly observations over each larger period. The sample foreach dataset is the largest available that overlaps with our uncertainty estimates: 1960:07-2011:12 (monthly),1961:Q3-2011:Q3 (quarterly), 1960:H2-2011:H2 (half-years), 1960-2009 (annual).
Average R2 From Regressions of Individual Uncertainty on Macro UncertaintyAverage: Uy(h) = 1
Ny
∑Ny
j=1 Ujt(h) PC: Uy(h) =∑Ny
j=1 wjUjt(h)
h R2 full sample R2 recession R2 non-recession R2 full sample R2 recession R2 non-recession1 0.18 0.19 0.12 0.17 0.17 0.122 0.22 0.24 0.15 0.22 0.24 0.153 0.24 0.26 0.16 0.23 0.25 0.164 0.25 0.26 0.17 0.23 0.24 0.165 0.26 0.27 0.18 0.24 0.25 0.166 0.27 0.28 0.19 0.25 0.26 0.167 0.28 0.29 0.19 0.25 0.27 0.178 0.29 0.30 0.20 0.25 0.27 0.179 0.29 0.30 0.20 0.25 0.28 0.1710 0.29 0.31 0.21 0.25 0.28 0.1711 0.30 0.31 0.21 0.25 0.29 0.1712 0.30 0.31 0.21 0.25 0.29 0.17
Table 2: Cross-sectional averages of R2 values from regressions of Uyjt(h) on the benchmark (average across
series) macro uncertainty measure Uyt (h) or the principal components (PC) macro uncertainty measure Uyt (h)over different subsamples. Uncertainty is estimated from the monthly, macro dataset. Recession months aredefined according to the NBER Business Cycle Dating Committee. The data are monthly and span the period1960:07-2011:12.
Relative Importance of Uncertainty v.s. FFR in VAR-11
Fraction Variation in Production (%)Explained by: Uyt (1) FFR Uyt (3) FFR Uyt (12) FFR VXO FFRk = 3 1.78 0.06 2.08 0.04 2.13 0.02 0.48 0.01k = 12 11.29 5.86 15.79 5.27 15.22 4.00 0.91 7.17k =∞ 7.87 33.67 8.79 31.39 15.76 28.96 6.93 39.07max k 174 ∞ 171 ∞ 174 ∞ 184 ∞k = max 17.02 33.67 20.86 31.39 28.54 28.96 6.93 39.07
Fraction Variation in Employment (%):Explained by: Uyt (1) FFR Uyt (3) FFR Uyt (12) FFR VXO FFRk = 3 0.90 0.06 0.98 0.03 0.86 0.01 1.06 0.02k = 12 9.15 6.99 13.23 6.33 13.08 4.87 1.11 8.26k =∞ 6.66 36.02 7.51 33.14 14.25 31.89 7.64 39.47max k 105 185 106 190 107 357 184 148k = max 16.40 41.30 20.06 39.35 31.00 34.83 7.64 52.74
Fraction of Variation in Hours (%):Explained by: Uyt (1) FFR Uyt (3) FFR Uyt (12) FFR VXO FFRk = 3 1.76 0.44 1.88 0.48 1.26 0.56 0.12 0.72k = 12 8.11 4.58 11.36 4.30 10.53 3.54 1.16 6.36k =∞ 7.38 12.92 8.98 12.08 11.93 9.79 2.15 17.21max k 21 ∞ 16 ∞ 37 ∞ 43 ∞k = max 9.21 12.92 11.96 12.08 12.34 9.79 2.32 17.21
Table 3: Decomposition of variance in production, employment and hours due to either uncertainty orthe federal funds rate in VAR-11. The VAR uses variables in the following order: log(industrial production),log(employment), log(real consumption), log(implicit consumption deflator), log(real value new orders, con-sumption and non-defense capital goods), log(real wage), hours, federal funds rate (FFR), log(S&P 500 Index),growth rate of M2, and uncertainty , where the latter is either Uyt (h) or the VXO Index. We estimate separateVARs in which uncertainty is either one of Uyt (h), h = 1, 3, 12 or the VXO index. Each panel shows the fractionof forecast-error variance of the variable given in the panel title at VAR forecast horizon k that is explained bythe uncertainty measure, as named in the column, or the FFR for that VAR. The row denoted “max k”gives thehorizon k for which the uncertainty variable named in the column explains the maximum fraction of forecasterror variance. The row denoted “k = ”max gives the fraction of forecast error variance explained at max k.Real variables are obtained by dividing nominal values by the PCE deflator. The data are monthly and spanthe period 1960:07-2011:12.
Average R2 From regressions of Firm-Level Uncertainty on Common UncertaintyAverage: Uy(h) = 1
Ny
∑Ny
j=1 Ujt(h) PC: Uy(h) =∑Ny
j=1 wjUjt(h)
h R2 full sample R2 recession R2 non-recession R2 full sample R2 recession R2 non-recession
1 0.15 0.29 0.14 0.12 0.27 0.112 0.18 0.34 0.16 0.16 0.32 0.143 0.19 0.35 0.17 0.17 0.33 0.154 0.20 0.36 0.18 0.18 0.33 0.165 0.21 0.36 0.18 0.18 0.33 0.166 0.21 0.36 0.19 0.18 0.32 0.16
Table 4: Cross-sectional averages of R2 values from regressions of Uyjt(h) on the benchmark (average across
series) macro uncertainty measure Uyt (h) or the principal components (PC) macro uncertainty measure Uyt (h)over different subsamples. Uncertainty estimated from the quarterly firm-level dataset with observations onfirm profit growth rates normalized by sales. Recession months are defined according to the NBER BusinessCycle Dating Committee. The data are quarterly and span the period 1970:Q3-2011:Q2.
Uy
t (12)
Uy
t (3)
Uy
t (1)
1965 1970 1975 1980 1985 1990 1995 2000 2005 20100.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5h = 1, corr with IP = −0.62h = 3, corr with IP = −0.61h = 12, corr with IP = −0.57
Figure 1: Aggregate Uncertainty: Uyt (h) for h = 1, 3, 12. Horizontal lines indicate 1.65 standarddeviations above the mean of each series. Industrial Production (IP) growth is computed asthe 12-month moving average of monthly growth rates (in percent). The data are monthly andspan the period 1960:07-2011:12.
F1t : Stock Returns
1970 1980 1990 2000 20100
0.5
1
1.5F2t : Real Activity
1970 1980 1990 2000 20100
0.1
0.2
F4t : Inflation
1970 1980 1990 2000 20100
0.1
0.2
F5t : FF Factors and Bond Spreads
1970 1980 1990 2000 20100
0.1
0.2
F2
1t
1970 1980 1990 2000 20100
2
4G1t
1970 1980 1990 2000 20100
0.5
1
1.5
Figure 2: Predictor Uncertainty: This plot displays uncertainty estimates for 6 of the 14predictors contained in the vector Zt ≡ (F ′t ,W
′t)′. Ft denotes the 12 factors estimated from Xit,
andWt ≡ (F 21t, G1t)
′, where G1t is the first factor estimated from X2it. Titles represent the types
of series which load most heavily on the factor plotted; “FF Factors”means the Fama-Frenchfactors (HML, SMB, UMD). The data are monthly and span the period 1960:07-2011:12.
IP: total
1970 1980 1990 2000 20100
1
2
3Emp: mfg
1970 1980 1990 2000 20100
1
2
3
Housing Starts: nonfarm
1970 1980 1990 2000 20100
1
2
3BaselineNo predictors
Consumer expect
1970 1980 1990 2000 20100
1
2
3
M2
1970 1980 1990 2000 20100
1
2
3CPI−U: all
1970 1980 1990 2000 20100
2
4
10 yr−FF spread
1970 1980 1990 2000 20100
2
4CP−FF spread
1970 1980 1990 2000 20100
2
4
Figure 3: The Role of Predictors: These plots display two estimates of Uyjt(1) for severalkey series in our data set. The first is constructed using the full set of predictor variables(“Baseline”); the second is constructed using no predictors (“No predictors”). The data aremonthly and span the period 1960:07-2011:12.
No Predictors
AR only
Baseline
1965 1970 1975 1980 1985 1990 1995 2000 2005 20100.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
Figure 4: Uncertainty in the S&P 500 Index. These plots show estimates of UySP500,t(1) forthe S&P 500 Index based on three different forecasting models. “No Predictors”indicates thatno predictors were used, “AR only” indicates that only a fourth-order autoregressive modelwas used to generate forecast errors, and “Baseline” indicates that the full set of predictorvariables was used to generate forecast errors. The data are monthly and span the period1960:07-2011:12.
Uy
t (1)
VXO
Correlation = 0.45
1.65 std
Bloom dates
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010−2
−1
0
1
2
3
4
5
6
7
Figure 5: Stock Market Implied Volatility and Uncertainty: This plot shows Uyt (1) and theVXO index, expressed in standardized units. The vertical lines correspond to the 17 datesin Bloom (2009) Table A.1, which correspond to dates when the VXO index exceeds 1.65standard deviations above its HP (Hodrick and Prescott, 1997) filtered mean. The horizontalline corresponds to 1.65 standard deviations above the unconditional mean of each series (whichhas been normalized to zero). The data are monthly and span 1960:07-2011:12.
0 20 40 60−4
−2
0
2Production
h =
1
0 20 40 60−4
−2
0
2Employment
0 20 40 60−4
−2
0
2
h =
3
0 20 40 60−4
−2
0
2
0 20 40 60−4
−2
0
2
h =
12
0 20 40 60−4
−2
0
2
0 20 40 60−4
−2
0
2
VX
O In
dex
0 20 40 60−4
−2
0
2
Figure 6: Impulse response of production and employment from estimation of VAR-11 usingUyt (h) or VXO as uncertainty. Dashed lines show 68% standard error bands. The data aremonthly and span the period 1960:07 to 2011:12.
0 20 40 60−4
−2
0
2Production
h =
1
0 20 40 60−4
−2
0
2Employment
0 20 40 60−4
−2
0
2
h =
3
0 20 40 60−4
−2
0
2
0 20 40 60−4
−2
0
2
h =
12
0 20 40 60−4
−2
0
2
0 20 40 60−4
−2
0
2
VX
O In
dex
0 20 40 60−4
−2
0
2
Figure 7: Impulse response of production and employment from estimation of VAR-8 usingUyt (h) or VXO as uncertainty. Dashed lines show 68% standard error bands. The data aremonthly and span the period 1960:07 to 2011:12.
Returns
1970 1980 1990 2000 2010−2
0
2
4
6Profits
Uy
t (1)
1970 1980 1990 2000 2010−2
0
2
4
6
Forecasts
1970 1980 1990 2000 2010−2
0
2
4
6TFP
1970 1980 1990 2000 2010−2
0
2
4
6
Figure 8: Cross-sectional Dispersion and Uncertainty: This plot shows Uyt (1) and fourdispersion-based proxies, expressed in standardized units. The proxies are (in clockwise or-der from the northwest panel) the cross-sectional standard deviation of: monthly firm stockreturns (CRSP), quarterly firm profit growth (Compustat), yearly SIC 4-digit industry totalfactor productivity growth (NBER-CES Manufacturing Industry Database), and half-yearlyGDP forecasts (Livingston Survey). The sample for each dataset is the largest available thatoverlaps with our uncertainty estimates: 1960:07-2011:12 (monthly), 1961:Q3-2011:Q3 (quar-terly), 1960:H2-2011:H2 (half-years), 1960-2009 (annual).
0 20 40 60
−5
0
5
Ret
urns
Months
Production
0 20 40 60
−5
0
5
Employment
0 5 10 15 20
−5
0
5
Pro
fits
Quarters0 5 10 15 20
−5
0
5
0 5 10
−5
0
5
For
ecas
ts
Half−years0 5 10
−5
0
5
0 5 10−10
−5
0
5
TF
P
Years0 5 10
−10
−5
0
5
Figure 9: Impulse response of production and employment from estimation of VAR-11 us-ing four dispersion measures Dt as uncertainty: (i) “Returns”is the cross-sectional standarddeviation of firm stock returns; (ii) “Profits”is the cross-sectional standard deviation of firmprofits; (iii) “Forecasts”is the cross-sectional standard deviation of GDP forecasts from theLivingston Survey; (iv) “TFP”is the cross-sectional standard deviation of industry-level totalfactor productivity. Dashed lines show 68% standard error bands. The sample for each datasetis the largest available that overlaps with our uncertainty estimates: 1960:07-2011:12 (monthly),1961:Q3-2011:Q3 (quarterly), 1960:H2-2011:H2 (half-years), 1960-2009 (annual).
Uy
t (4)
Uy
t (2)
Uy
t (1)
DBt
1975 1980 1985 1990 1995 2000 2005 20100.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2Dispersion firm profits, corr with IP = −0.14h = 1, corr with IP = −0.23h = 2, corr with IP = −0.26h = 4, corr with IP = −0.28
Figure 10: Firm-level Uncertainty: Uyt (h) for h = 1, 2, 4. Horizontal lines indicate 1.65 standarddeviations above the mean of each series. The thin solid line marked “Dispersion in firmprofits”is the cross-sectional standard deviation of firm profit growth, normalized by sales, anddenoted DBt . The dispersion is taken after standardizing the profit growth data. IndustrialProduction (IP) growth is computed as the 12-month moving average of monthly growth rates(in percent). The data are monthly and span the period 1970:Q3-2011:Q2.